bai toan lien quan kshs qua de thi dai hoc

8/7/2019 Bai Toan Lien Quan KSHS qua de thi Dai hoc

1/36

Kho st hm s v cc thi i hc 12 www.VNMATH.com

www.VNMATH.com www.VNMATH.com

Chuyn hm sChng 1

o hmA)Tnh o hm bng cng thc

BT11) )352)(43( 232 xxxxxy 2) )45)(34)(23)(12( xxxxy

3) 3223 )1(2)133( xxxxy

4) 3244 )14()23()12( xxxxy

5) 432 )4()2()1( xxxy

BT1

1) dcxbax

y

8753

x

xy

2)nmx

cbxaxy

2

43

652 2

x

xxy

3)pnxmx

cbxaxy

2

2

832

9452

2

xx

xxy

4)qpxnxmx

dcxbxaxy

23

23

5)x

xy

2

3

3

3

3

1

x

xy

6)13

3

xx

xxy

44

1

1

1

12

x

x

x

xy

7)332

1

75

1

453

x

x

x

xxy

BT3

1) xxxxxy

2)

1

3

2

x

xy

2

56

2

x

xy

3)1

1

x

xy

1

1

2

xx

xy

4)2

2

48

xxy

3 23 2

21

xxxy

5) 3 32 32)1( xxxy

6)2

32

)1(

)3)(2(

x

xxy

3)5( 2 xxy

7)x

xy

1

1

29 x

xy

8)3

111

xxxy 3

3

3

1

1

x

xy

BT4)cos(sin)sin(cos xxy

xxxy 2cossin.222

xxxxy sin.2cos).2(2

xxxxy

cossincossin

23 cossin xxy

nxxyn cos.sin nxxy n sin.cos

xxy 3cos3sin 55

xxx

xxxy

cossin

cossin

4cot

2

xg

xtgy

3 83 3 cotcot.4 xgxgy

xxx

xxxy

sincos

sincos2

2

xtgxtgtgxy53

51

31

Chng 2

Tnh n iu ca hm s1)-Tm iu kin ca tham s hm s

n iuA1)Hm a thcBT1 (H Ngoi Thng 1997)

Tm m mxmxxy 4).1(3 23 nghch bin (-1;1)

BT2Tm m 2).512().12(3 23 xmxmxy

ng bin trn (-;-1) U [2; +)

BT3

Tm m mxmxmmxy ).1().1(23

1 23

ng bin trn (-;0) U [2; +)

BT4Tm m 1).512(26 23 xmmxxy

ng bin trn (-;0) U (3; +)

BT5 (H Thu Li 1997)

Tm m xmxmxm

y ).23(..3

1 23

ng bin trn R

BT6

Tm m )32).(1(2).772( 223 mmxmmmxxy

ng bin trn [2; +)

BT7


2/36



Tm m 7).2.().1(3

1 23 xmmxmxy

ng bin trn [4; 9 ]BT8

Tm m 2223

).34().1(3

2mxmmxmxy ng

bin trn [1; +)BT9

Tm m 1).232()1( 223 xmmxmxy

ng bin trn [2; +)

BT10 (H Lut Dc 2001)Tm m

1).2(3)1(3 23 xmmxmxy ng bin

trong cc khong tho mn 21 x

BT11 (HVQHQT 2001)Tm m 9).4()1( 223 xmxmxy

ng bin vi mi x

A2)Hm phn thc

BT1 (H TCKT 1997)

Tm m 1

.32 2

x

mxxy ng bin

trn (3; +)BT2 (H Nng Nghip 2001)

Tm m 12

.32 2

x

mxxy nghch

bin trn

;

2

1

BT3

Tm m x

xmmxy

3)1(2 ng

bin trn (4; +)BT4

Tm m 1

.53)12( 2

x

mxxmy nghch

bin trn [ 2;5 ]BT5

Tm m mx

mmxxy

2

32 22

ng bin

trn (1; +)

BT6 (H Kin Trc 1997)Tm m

mx

mmxxy

222ng

bin trn (1; +)BT7 (H Nng 1998)

Tm m 1

22 2

mx

mmxxy ng

bin trn (1; +)BT8 (H TCKT 2001)

Tm m

mx

mmmxxmy

)2(2)1( 232nghch bin

trn tp xc nh

A3)Hm lng gic

BT1Tm m xmxmy cos).12()3( lun

nghch bin

BT2Tm a, b xxbxay 2cos.sin. lun

ng bin

BT3Tm m xxxxmy 3sin

9

12sin.

4

1sin.

lun ng bin

BT4Tm m

xxxmxxmy 2cos.4

1cos.sin.cos2.2 22 lun

ng bin

BT5Tm a

1).2sin4

3().cos(sin

2

1.

3

1 23 xaxaaxy lun

ng bin

BT6Tm m )cos(sin xxmxy lun ng

bin trn RBTBS

1) Tm a 3

21 3 4

3

x y a x a x ng

bin trn ;3o

HD: 2 2 3

' 0 , / 0;32 1

x x y a g x x

x

2) Tm m hm s 3 23 y x x mx m nghchbin trn mt on c di bng 1

2)- S tnh n iu gii phngtrnh ,bt phng trnh ,h phng

trnh , h bt phng trnh

BT1 (H Thu Li 2001)

GPT : 21 )1(222

xxxx


3/36



BT2GBPT :

275log155log 2322 xxxx BT3

GHBPT :

013

0123

3

2

xx

xx

BT4(HKT 1998)

GHBPT :

01093

045

23

2

xxx

xx

BT5

GHBPT :

09533

1

0)(loglog

23

2

2

2

2

xxx

xx

BT6(HNT HCM 1996)

GHPT :

2

2

2

23

23

23

xxxz

zzzy

yyyx

BT7

GHPT :

xzzzz

zyyyy

yxxxx

)1ln(33

)1ln(33

)1ln(33

23

23

23

BT8

GHPT :

x

z

y

zz

yy

xx

23

23

23

2

2

2

4

1

4

1

4

1

BT9

GHPT :

xx

z

zz

y

yy

x

sin6

sin6

sin6

3

3

3

BT10GBPT 4259 xx

BT11Tm m BPT

131863 22 mmxxxx Lun ng vi mi x thuc [ -3; 6]

BT12

Tm m x

mxmxx1

).1(2 23

ng vi mi x 2

BT13 (HBK 2000)Tm a BPT 323 )1.(13 xxaxx cnghim

BT14 (H Lut 1997)

Tm m BPT3

3 12.3x

xmx

ng vi

mi x 1

BT15Tm a )45(12 xxmxxx

c nghim

Chng 3

Cc tr ca hm s1)- Gi tr ln nht gi tr nh nht

ca hm sBT1

Tm Max,Min caxx

xxy

44

66

cossin1

cossin1

BT2 (HSP1 2001)

Tm Max,Min caxxxxy

24

24

cos2sin3sin4cos3

BT3

a)Tm Max,Min ca )cos1(sin xxy

b) Tm Max,Min ca xxy 2sin3sin

BT4

Tm Max,Min caxx

ycos4

1

sin4

1

BT5Tm Max,Min ca

atgx

tgxa

x

xy

1

1)1(

2sin1

2sin1

vi

4;0

x

BT6

a)Tm Max,Min ca xxy 33 cossin

b)Tm Max,Min ca

xxxy 3cos3

12cos

2

1cos1


4/36



c)Tm Max,Min ca

xxxxy 4cos4

13cos

3

12cos

2

1cos1

d)Tm Max,Min ca xxxy sin2cossin

BT7

Tm Max,Min ca

xx

xxxxysincos

sincoscos.sin 66

BT8 (HBK 1996)

Cho2

0

x v 2 m , Zn

Tm Max,Min ca xxy nm cos.sin

BT9

Cho 1 a Tm Min ca

xaxay sincos Tm Max,Min ca

xxy sin.21cos.21

BT10

Gi s 012

46122

22 m

mmxx c

nghim x1, x2 Tm Max,Min ca3

2

3

1 xxS

BT11

Tm Max,Min ca 22

22

4)4(

yxyxxS

Vi x2 + y2 > 0

BT12 (HVQHQT 1999)

Cho x,y 0 , x+y=1

Tm Max,Min ca11

x

y

y

xS

BT13 (HNT 1999)

Cho x,y 0 , x+y=1

Tm Max,Min ca yxS 93

BT14 (HNT 2001)

Cho x,y > 0 , x+y=1

Tm Min cay

y

x

xS

11

BT15 (H Thng mi 2000)

Tm Max,Min ca

xxaxxy cos.sin.cossin 66

BT16 (HVQY 2000)

Tm Max,Min ca

1cos.sincossin 44 xxxxy

BT17 (H Cnh St 2000)

Tm Max,Min ca xxy 5coscos5

Vi

4;

4

x

BT18 (HQG TPHCM 1999)

Cho mxxxxxf 2sin3)cos.(sin22cos)( 32

Tm Max,Min ca f(x) . T tm m xxf .36)(

2

BTBS

Tm GTNN 3 23 72 90 5;5 y x x x x

Tm GTNN1 1 1

y x y z x y z

tho mn

3, , , 0

2 x y x voi x y z

HD: Csi 3 33

3 13 (0; ]

2P xyz Dat t xyz

xyz

Tm GTLN, GTNN ca hm s

2 2

2 4sin cos 1

1 1

x xy

x x


2cos 04

y x x x

Tm GTLN ca hm s2sin , ;

2 2 2

x y x x


34

2sin sin en 0;3

y x x tr

Tm GTLN, GTNN ca hm s2

3ln 1;x

y tren ex

2)- S dng GTLN, GTNN ca hm strong phng trnh, bpt ,hpt, hbpt

BT1

GPT:16

1)1( 55 xx

BT2(H Thu Sn 1998)

Tm m phng trnh sau c nghim

mxxxx )2)(2(22

BT3(H Y TPHCM 1997)Tm m phng trnh sau c nghim

a) mxxxx 99 2


5/36



b) mxxxx )6)(3(63

BT4

Tm m bt phng trnh sau c nghim

13. mxxm

BT5(HQG TPHCM 1997)

Tm m 42)1(222

xxmx ng vi mi x thuc [0;1]

BT7(HGT 1997)

Tm m )352()3).(21( 2 xxmxx

ng

3;

2

1x

BT8

Tm m phng trnh sau c 4 nghim phnbit

mxxxxxx 42224)22( 2232

BT9

Tm a d BPT sau ng vi mi x thuc R0122436cos.15sin363cos5cos3 224 aaxxxx

BT10

a)Tm m mxxxx 2)6)(4( 2

ng vi mi x thuc [-4;6]

b) Tm m 182)2)(4(4 2 mxxxx

ng vi mi x thuc [-2;4]

BT11(HQG TPHCM 1998)

Tm a phng trnh c nghim duy nht

axxx

x

12

12

13 2

BT12 (H QGTPHCM 1997-1998)

a) Tm m d phng trnh sau c nghim

mxxxxx 4sin)cos(sin4)cos(sin426644

b) Tm m d phng trnh sau c nghim

mxxx cos.sin.64cos

c)Tm m d phng trnh sau c nghimxmxx 4cos.cossin 2244

BT13 (H Cn Th 1997)

Tm m d phng trnh sau c nghim

xxmxxx 2cos31.cos2cossin2cos3 22446

BT14(HGT 1999)a)Tm m 02cos.sin42cos. mxxxm

C nghim

4;0

x

b)Tm m mxxx 3sin.2cos.sin

C ng 2 nghim

2;

4

x

BT15


6

9.69.6mx

xxxx

BT16

Tm a bt phng trnh sau ng vi mi xthuc R 13)1(49. aaa xx

BT17

Tm a bt phng trnh sau c nghim

).(log1log 222 axax BT18

Tm a h bt ph

ng trnh sau c nghim

01.3

0123

2

2

mxx

xx

3)- S dng GTLN, GTNN chng minh btng thc

BT1

CMR 13122 2 xx

Vi mi x thuc TX

BT2a)Tm m 282 xxm c 2 nghim phnbit

b)Cho a + b + c = 12 CMR

6.6888 222 cba

BT3

CMR3

24sin

4

13sin

3

12sin

2

1sin xxxx

vi

53;

5

x

BT4

CMR

1123cos2cos6cos4cos17 22 aaaa

BT5

CMR33

22sin

xxx

vi

2;0

x

BT6CMR 3)()(2 222333 xzzyyxzyx

vi 1,0,, zyx

BT7


6/36



CMR

ABC

CAAgCgBgA

sin

1

sin

1

sin

1233cotcotcot

4)- Cc tr hm bc 3Xc nh cc tr hm s

BT1Tm m cc hm s c cc i cc tiu

1) )12().6(.3

1 23 mxmmxxy

2) 5.3).2( 23 xmxxmy

BT2(HVNgn Hng TPHCM 2001)

CMR vi mi m hm s sau lun dt cc trti x1; x2 vi x1x2 khng ph thuc m

1)1.(6)12(3.2 23 xmmxmxy

BT3

Tm m hm s sau lun t cc tr ti x1;x2 tho mn x1 < -1 < x2 khng ph thuc m

1).45()2(.3

1 223 mxmxmxy

BT4(CSP TPHCM 1999)

Tm m mxmmxxy )1(33 223 tcc tiu ti x = 2

BT5(H Hu 1998)Tm m 2)1(3 23 xmmxxy t cc

tiu ti x = 2

BT6(H Bch Khoa HN 2000)

Tm m 1)1(3 23 xmmxmxy khngc cc tr

Phng trnh ng thng i qua cc i cctiu

BT7(H Thu Sn Nha Trang 1999)

Cho hm s1).(12)13(3.2 223 xmmxmxy

Tm m hm s c C,CT .Vit phngtrnh ng thng i qua C,CT

BT8(HVKT Mt m 1999)

Cho hm s)2(2)27(2)1(3 223 mmxmmxmxy

Tm m hm s c C,CT .Vit phngtrnh ng thng i qua C,CT

BT9

Tm m 323 43)( mmxxxf c C,CTi xng nhau qua ng thng y = x

BT10(H Dc HN 2000)

Tm m 1)1(6)12(32)( 23 xmmxmxxf c

C,CT i xng nhau qua ng thng y = x + 2

BT11(HQG TPHCM 2000)

Cho (Cm) : mxmmxmxy 3)12(323

Tm m (Cm ) c C v

CT . CMR khi ng thng i qua C, CT lun di qua mt imc nh

BT12

Tm a hm s sau lun t cc tr ti x1; x2tho mn 122

2

1 xx

1).2cos1()sin1(2.3

4 23 xaxaxy

BT13

Cho hm sxaxaaxy .2sin

4

3)cos(sin

2

1.

3

1 23

1)Tm a hm s lun ng bin

2)Tm a hm s t cc tr ti x1; x2 tho mn

21

2

2

2

1 xxxx

BT14

Tm m hm s mxm

xy 232

3

C cc im C v CT nm v 2 pha ca ngthng y = x

5)- Cc tr hm bc 4BT1

Tm m hm s sau ch c cc tiu mkhng c cc i

4)12(3.8 234 xmxmxy

BT2

CMR hm s 15)(234

xxxxf C 3 im cc tr nm trn mt Parabol

BT3

Cho (Cm) :124643)( 234 mxmxmxxxfy

Bin lun theo m s lng Cc i, cc tiu ca(Cm)

Tm m hm s t cc tiu ti 2;20 x

BT3Cho (Cm) :

1).6()2(2

32.

4

1)( 234 xmxmxxxfy


7/36



Tm m hm s c 3 cc tr

Vit phng trnh Parabol i qua 3 im cc trca (Cm)

BT4(H Cnh st 2000)

Tm m hm s sau ch c cc tiu m

khng c cc i2

3

4

1 24 mxxy

BT5 (H Kin trc 1999)

Tm m )21()1()( 24 mxmmxxf cung mt cc tr

6)- Cc tr hm Phn thc bc 2 / bc 1

6.1-S tn ti cc trng thng

i qua C,CT

BT1

Tm m cc hm s sau c cc tr

1

2 222

x

mxmxy

1

)2(2

x

mxmxy

mx

mmxxy

22(H SPHN 1999)

1

)1(2

x

mxmxy (C SPHN 1999)

2

1)1(2

mx

xmmxy

(H Y Thi Bnh 1999 )

1

)1)(2(2 222

mx

mxmxmy

(H Thi Nguyn 2000)

BT2 (H TCKT 1999)

Cho (Cm) :mx

mmxxy

22

Tm m hm s c C, CT

Vit phng trnh ng thng i qua C, CT

BT3 (H Dn lp Bnh Dng 2001)

Cho (Cm) :1

23)2(2

x

mxmxy

Tm m hm s trn c C, CT

BT4

Tm a ax axxy sin.2 1cos.22

c C , CT

BT5

Tm a ax

aaaxaxy

cos

sincos.sincos. 22

c C , CT

BT6 (H Cnh st 2000)

Vit phng trnh ng thng i qua C,CT

ca :mx

mxxy

82

BT7

Cho (Cm) :mx

mmmxxmy

)2(2)1( 232

(m#-1)

Tm m hm s c t cc tr ti cc imthuc ( 0 ; 2 )

BT8

Tm a,b,c 2

2

x

cbxaxy c cc tr bng

1 khi x=1 v ng tim cn xin ca th

vung gc vi ng2

1 xy

6.2-Qu tch cc im cc tr trn mtphng to

BT9 (H Nng 2000)

Cho hm s (Cm) :1

12

x

mmxxy

Tm m hm s c cc tr. Tm qu tch caim cc tr (Cm)

BT10 (H Thu Sn TPHCM 1999)

Cho hm s (Cm) :1

222

x

mmxxy

Tm m hm s c cc tr. CMR cc imcc tr ca (Cm) lun nm trn mt Parabol cnh

BT11 (H Ngoi Ng 1997)

Cho hm s (Cm) :2

422

x

mmxxy

Tm m hm s c C,CT. Tm qu tch caim C

BT12

Cho hm s (Cm) :

mx

mxmmxy

1)1( 422

CMR: trn mt phng to tn ti duy nhtmt im va l im C ca th ng vi mno ng thi va l im CT ng vi gi trkhc ca m

6.3-Biu thc i xng ca cc a, cc tiu


8/36



BT13

Tm m mx

mxxy

32 2c C,CT v

8CTCD yy

BT14

Tm m 2)1(

2)1( 2

xm

xxm

y c C,CT v

08)1)(( myy CTCD

BT15 (HSP1 HN 2001)

Tm m 1

222

x

mxxy c C,CT v

khong cch t 2 im n ng thngx + y + 2=0 l bng nhau

BT16

Tm m 2 23)2(2

x

mxmxy c

C,CT ng thi tho mn2

122 CTCD yy

6.4-V tr tng i ca cc im C - CT

BT17 (H Cn Th 1999)

Cho :mx

mmxmxy

4)32( 22

Tm m hm s c 2 cc tr tri du nhau

BT18 (H QG 1999)

Cho :1

2

x

mxxy

Tm m hm s c 2 cc tr nm v 2 phai vi trc Oy

BT19 (H Cng on 1997)

Cho hm s :mx

mmxxy

2

(m#0)

Tm m hm s c 2 cc tr tri du nhau

BT20 (H Thng Mi 1995)

Cho hm s :1

122

x

mmxxy

Tm m C,CT v 2 pha i vi trc Ox


Cho hm s :mx

mxmxy

1)1(2

Tm m hm s c C,CT v YC. YCT>0

BT22

Tm m :mx

mmxxy

52c C,CT cng

du

BT23

Tm m :1

2

x

mmxxy c C,CT nm v

2 pha ca ng thng x-2y-1=0

BT24

Tm m :mx

mmxmmxy

2

322)14(2 322

c mt cc tr thuc gc (II) v mt cc tr thucgc (IV) trn mt phng to

BT25

Tm m :1

244)1( 22

mx

mmxmxy c

mt cc tr thuc gc (I) v mt cc tr thuc gc(III) trn mt phng to

7)- Cc tr hm Phn thc bc 2 / bc 2

BT1

Lp bng bin thin v tm cc tr

1

122

2

xx

xxy

2

432

2

xx

xxy

682

81032

2

xx

xxy

BT2

Tm m,n 12

22

2

xx

nmxxy t cc i bng

4

5khi x= - 3

BT3

1)Vit phng trnh ng thng i qua

C,CT camxx

xxy

54

1322

2

(m>1)

2)Vit phng trnh ng thng i qua

C,CT camxx

xxy

23

522

2

3)Tm a,b 12

xx

baxy c ng mt cc

tr v l cc tiu

8)- Cc tr hm s cha gi tr tuyt iv hm v t

BT1

Tm cc tr hm s sau 532 2 xxy

BT2 (H Ngoi Thng 1998)


9/36



Tm m phng trnh

15

1 24342

mm

xx

c 4 nghim phn bit

BT3 (H Kinh T 1997)

Cho 90723)( 23 xxxxf

Tm

5;5

)(

x

xMaxf

BT4

Tm m phng trnh

mm

xxx

2

296 23

2

1

c 6 nghim phn bit

BT5

Tm m phng trnhmxxxx 545.2 22

c 4 nghim phn bit

BT6

Tm cc tr hm s sau

1) 5432 2 xxxy

2) 11 22 xxxxy

BT71)Tm a hm s 12 2 xaxy c

cc tiu

2)Tm a hm s

5422 2 xxaxy c cc i

BT8

Lp bng bin thin v tm cc tr hm s sau

1) 2531 2 xxy

2) 2103 xxy

3) 3 3 3xxy

4)x

xxy

1

1.

9)- Cc tr hm lng gic

hm s M,lgarit

BT1Tm cc tr hm s

xgx

xy .cot2

sin

cos3

1coscos2 xxy

xxxy 3cos.3

12cos.

2

1cos1

1sin

2sin

x

xy

)sin1(cos xxy

xxy 33 cossin BT2

Tm a hm s xxay 3sin.3

1sin. t

C ti3

x

BT3

Tm cc tr hm s

1)

xexy .1

2

2) 12

).1(

xxx

exy

3) xey x ln.

4)x

xy

lg

5)

0xkhi0

x#0)(Khi1

sin2

1

xe

yx

Chng 5

Cc bi ton v Tip tuyn1)- tip tuyn ca a thc bc ba

Dng 1 Phng trnh tip tuyn ti mt imthuc th


Cho (Cm) 1)(23 mxxxfy

Tm m (Cm) ct ng thng y=-x+1 ti 3im phn bit A(0,1) , B, C sao cho tiptuyn vi (Cm) ti B v C vung gc vi nhau

BT2 (HVCNBCVT 2001)

Cho hm s (C) xxxfy 3)( 3

CMR ng thng (dm) y=m(x+1) + 2 lun ct

(C ) ti im A c nhTm m (dm) ti 3 im phn bit A , B, C sao

cho tip tuyn vi th ti B v C vunggc vi nhau


10/36



BT3 (H Ngoi Ng HN 2001)

Cho (C)3

2

3

1)( 3 xxxfy

Tm cc im trn (C) m tip tuyn ti

vung gc vi ng thng3

2

3

1 xy

BT4

Cho hm s (C) 13)( 23 xxxfy

CMR trn (C) c v s cc cp im m tiptuyn ti tng cp im song song vi nhaung thi cc ng thng ni cc cp tip imny ng qui ti mt im c nh

BT5

Cho hm s (C))0#(a)( 23 dcxbxaxxfy

CMR trn (C) c v s cc cp im m tiptuyn ti tng cp im song song vi nhaung thi cc ng thng ni cc cp tip imny ng qui ti mt im c nh

BT6 (H Ngoi Thng TPHCM 1998 )

Cho hm s (C) 593)( 23 xxxxfy

Tm tip tuyn vi th ( C ) c h s gcnh nht

BT7 (HV QHQT 2001)

Cho (C) 131)( 23 mxmxxxfy

Tm tip tuyn vi th ( C ) c h s gcnh nht

BT8 (HV CNBCVT 1999 )

Gi s A,B,C thng hng v cng thuc th(C ) 23)( 3 xxxfy Cc tip tuyn vi(C ) ti A,B,C ct th (C) ti A1,B1,C1

CMR Ba im A1,B1,C1 thng hng

BT9

Cho

8652:)(

474:)(

23

2

23

1

xxxyC

xxxyCVit phng

trnh tip tuyn ca (C1) , (C2) ti cc giao imchung ca (C1) v (C2)

BT10 (H KTQDHN 1998 )

CMR trong tt c cc tip tuyn ca

(C) 393)( 23 xxxxfy , tip tuyn

ti im un c h s gc nh nhtBT11 (HV Qun 1997 )

Cho (C) )1(1)( 3 xkxxfy ,

Vit phng trnh tip tuyn (t) ti giao imca (C) vi Oy

Tm k (t ) chn trn Ox ,Oy mt tam gicc din tch bng 8

BT12 (H An Ninh 2000 )

Cho (C) 1)( 23 mmxxxfy ,

Vit ph

ng trnh tip tuyn (t) ti cc im cnh m h (C) i qua

Tm qu tch giao im ca cc tip tuyn

BT13 (H Cng on 2001 )

Tm im M thuc (C) 11232 23 xxxy sao cho tip tuyn ca (C ) ti im M i quagc to

Dng 2 Vit phng tip tuyn trnh theo hs gc cho trc

BT1Cho (C) 73)( 3 xxxfy ,

1)Vit phng trnh tip tuyn vi (C) bit tiptuyn ny song song vi y= 6x-1

2)Vit phng trnh tip tuyn vi (C) bit tip

tuyn vung gc vi 29

1 xy

3)Vit phng trnh tip tuyn vi (C) bit tiptuyn to vi y=2x+3 gc 45 0

BT2(H M Thut Cng nghip HN 1999)Cho (C) xxxfy 3)( 3 ,Vit phng trnh tip tuyn vi (C) bit tip

tuyn ny song song vi y= - 9.x + 1BT3(H M TPHCM 1999)

Cho (C) 23)( 23 xxxfy ,Vit phng trnh tip tuyn vi (C) bit tip

tuyn vung gc vi 5.y-3x+4=0BT4

Cho (C) 51232)( 23 xxxxfy ,

1)Vit phng trnh tip tuyn vi (C) bit tiptuyn ny song song vi y= 6x-4

2)Vit phng trnh tip tuyn vi (C) bit tip

tuyn vung gc vi 23

1 xy

3) Vit phng trnh tip tuyn vi (C) bit tip

tuyn to vi 52

1 xy gc 45 0

BT5

Cho (C) 423

1 23 xxxy ,


11/36



1)Vit phng trnh tip tuyn c h s gck =-2

2)Vit phng trnh tip tuyn to vi chiudng Ox gc 600

3)Vit phng trnh tip tuyn to vi chiudng Ox gc 150

4)Vit phng trnh tip tuyn to vi trc

honh gc 7505)Vit phng trnh tip tuyn to vi ng

thng y=3x+7 gc 450

6)Vit phng trnh tip tuyn to vi ng

thng 32

1 xy gc 300

Dng 3 Phng tip tuyn i qua mt imcho trc n th

BT1

Vit phng trnh tip tuyn i qua

1;3

2A

n 133 xxy

BT2(H Tng Hp HN 1994)

Vit phng trnh tip tuyn i qua A(2;0)

n 63 xxy

BT3(H Y Thi Bnh 2001)


n xxy 93

BT4(H An Ninh 1998)

Vit phng trnh tip tuyn i qua A(-1;2)

n xxy 33

BT5(HV Ngn Hng TPHCM 1998)


n 343 xxy

BT6 (HC BCVT TPHCM 1999)

Cho (C) 23)( 23 xxxfy . Tm ccim trn (C) k c ng mt tip tuyn ti th (C)

BT7 (H Dc 1996)

Cho (C) cbxaxxxfy 23)( . Tmcc im trn (C) k c ng mt tip tuynti th (C)


C bao nhiu tip tuyn i qua

34;

94A n

th (C) 4323

1 23 xxxy

BT9 (Phn Vin Bo Ch 2001)

C bao nhiu tip tuyn i qua A(1;-4) n th (C) 532 23 xxy

BT10

Tm trn ng thng y=2 cc im k c 3tip tuyn n th (C) 23 23 xxy

BT11( H QG TPHCM 1999)Tm trn ng thng x=2 cc im k c 3

tip tuyn n th (C) 23 3xxy

BT12( H Nng Lm 2001)

Tm tt c cc im trn trc honh m t kc 3 tip tuyn n th (C) 23 3xxy trong c hai tip tuyn vung gc vi nhau

2)- tip tuyn ca a thc bc bn

BT1 (H Hu khi D 1998)Cho (Cm) 122)(

24 mmxxxfy

Tm m cc tip tuyn vi th ti A(1;0),B(-1;0) vung gc vi nhau

BT2

Cho (Cm)2

53

2

1)( 24 xxxfy

1)Gi (t) l tip tuyn ca (C) ti M vi xM= a .CMR honh cc giao im ca (t) vi (C)l nghim ca phng trnh

0632 222 aaxax 2)Tm a (t) ct (C) ti P,Q phn bit khc M

Tm qu tch trung im K ca PQ

BT3 (H Thi Nguyn 2001)

Cho th (C) 24 2xxy .Vit phng

trnh tip tuyn ti 0;2A BT4(H Ngoi Ng 1999)

Cho th (C)4

92

4

1 24 xxy .Vit

phng trnh tip tuyn ti cc giao im ca (C)vi Ox

BT5

Vit phng trnh tip tuyn ca

(C) 52

1

3

1

4

1 234 xxxxy song song vi

ng thng y=2x-1

BT6Vit phng trnh tip tuyn ca


12/36



(C) 142 24 xxxy vung gc vi ng

thng 34

1 xy

BT7

Cho th (C) 732

1 234 xxxy .

Tm m th (C) lun lun c t nht 2 tiptuyn song song vi ng thng y=m.x

BT8

Cho th (Cm ) 124 mmxxy . Tm m

tip tuyn vi th ti A song song ving thng y=2.x vi A l im c nh chonh dng ca (Cm )

BT9

Cho (C) 242

1

2

1)( xxxfy

Vit phng trnh tip tuyn i qua im O(0;0)n th (C)

BT10 (H KT 1997)

Cho (C) 22 )2()( xxfy

Vit phng trnh tip tuyn i qua im A(0;4)n th (C)

BT11

Cho (C)2

33

2

1)( 24 xxxfy

Vit phng trnh tip tuyn i qua im

2

3;0A n th (C)

BT12

Cho (C) 12)( 24 xxxfy

Tm tt c cc im thuc Oy k c 3 tiptuyn n th (C)

3)- tip tuyn ca h

m phn thc bcnht/bc nhtDng 1 Phng trnh tip tuyn ti mt imthuc th

BT1(HVBCVT 1998)

Cho th1

1

x

xy CMR mi tip tuyn ca

(C) to vi 2 tim cn ca (C) mt tan gic cdin tch khng i

BT2

Cho th32

54

x

xy v im M bt k

thuc (C) . Gi I l giao dim 2 tim cn . tiptuyn ti M ct 2 tim cn ti A,B

1) CMR M l trung im AB

2) CMR din tch tam gic IAB khng i

3) Tm M chu vi tam gic IAB nh

nhtBT3

Cho th (Cm)mx

mxy

32Tm m tip

tuyn bt k ca (Cm) ct 2 ng thng timcn to nn 1 tam gic c din tch bng 8

BT4(H Thng Mi 1994)

Cho th (Cm)mx

mxmy

)13(Tm m

tip tuyn ti giao im ca (Cm) vi Ox songsong vi y= - x-5

BT5(H Lm Nghip 2001)

Cho th (C)3

13

x

xy V im M bt k

thuc (C) gi I l giao 2 tim cn .Tip tuyn tiim M ct 2 tim cn ti A v B

CMR M l trung im AB

CMR din tch tam gic IAB khng i

Dng 2 Vit phng trnh tip tuyn theo hs gc k cho trc

BT1

Cho th (C)45

32

x

xy Vit phng trnh

tip tuyn ca (C) vung gc vi ng thng (d)y= -2x

BT2

Cho th (C)1

34

x

xy Vit phng trnh

tip tuyn to vi ng thng (d) y= 3x gc 45 0

BT3

Cho th (C)52

73

x

xy Vit phng trnh

tip tuyn ca (C) khi bit

1)Tip tuyn song song vi ng thng

12

1 xy

2)Tip tuyn vung gc vi ng thngxy 4

3)Tip tuyn to vi ng thng y= -2x gc 450


13/36



4)Tip tuyn to vi ng thng y= -x gc600

BT4

Cho th (C)33

56

x

xy CMR trn th (C)

tn ti v s cc cp im sao cho tip tuyn ticc cp im ny song song vi nhau ng thi

tp hp cc ng thng ni cc cp tip imng qui ti mt im c nh

Dng 3 Phng tip tuyn i qua mt imcho trc n th

BT1(H Ngoi Thng TPHCM 1999)

Cho hm s (C)2

2

x

xy Vit phng trnh

tip tuyn i qua im A(-6;5) n th (C)

BT2(H Nng Nghip HN 1999)CMR khng c tip tuyn no ca th (C)

1

x

xy i qua giao im I ca 2 ng thng

tim cn

BT3(H Hu 2001 Khi D)

Vit phng trnh tip tuyn t im O(0;0)

n th (C)2

)1(3

x

xy

BT4

Tm m t im A(1;2) k c 2 tip tuyn

AB,AC n th (C)2

x

mxy sao cho tam

gic ABC u ( y B,C l 2 tip im)

4)- tip tuyn ca hm phn thc bchai/bc nhtDng 1 Phng trnh tip tuyn ti mt imthuc th

BT1(HVCNBCVT 1997)

Cho th1

12

x

xxy Tm M thuc th

(C) tip tuyn ti M ct Ox ,Oy ti im A,Bsao cho tam gic OAB vung cn

BT2(H Xy Dng 1993)

Cho th1

332

x

xxy CMR din tch tam

gic to bi 2 tim cn vi mt tip tuyn bt k

l khng iBT3(H QG 2000)

Cho th1

11

xxy Tm M thuc (C)

c xM > 1 sao cho tip tuyn ti im M to vi 2tim cn mt tam gic c chu vi nh nht

BT4(HSP TPHCM 2000)

Cho th1

222

x

xxy Gi I l tm i

xng ca th (C) v im M l mt trn (C)tip tuyn ti M vi (C) ct 2 ng thng timcn ti A,B CMR M l trung im AB v dn tchtam gic IAB khng ph thuc vo v tr im Mtrn (C)

BT5(HV Qun Y 2001)

Cho th2

52 2

x

xxy CMR ti mi im

thuc th (C) lun ct 2 tim cn mt tam gic

c din tch khng iBT6(C SPHN 2001)

Cho th2

332

x

xxy CMR tip tuyn ti

im M tu thuc th (C) lun to vi 2 timcn mt tam gic c din tch khng i

BT6(C SPHN 2001)

Cho th1

2

x

xy Tm im M thuc nhnh

phi ca th (C) tip tuyn ti M vung gcvi ng thng i qua M v tm di xng I ca(C)

5) - tip tuyn ca hm v tBT1(H Xy Dng 1998)

Cho th (C)2

3 3 2xxy

Vit phng trnh tip tuyn ca (C) song songvi y=k. x

Tm GTLN ca khong cch gia

ng thngy= k.x vi tip tuyn ni trn khi k 0,5

BT2Tm trn trc Oy cc im k n th

(C)9 2xy 2 tip tuyn vung gc vinhau

BT3

Cho th (C) 124 2 xxxy . Tmtrn trc tung cc im c th k t nht 1 tip

tuyn n (C)BT4


14/36



Cho th (C) 5312)( xxxfy .Vit phng trnh tip tuyn i qua im

4

27;2A n (C)

BT5

Cho th (C) 41)( 2xxxfy .

Vit phng trnh tip tuyn i qua im 221;1 A n (C)BT6

Cho th (C) 742)( 2 xxxxfy .Tm trn ng thng x=1 cc im c th kc tip tuyn n (C)

BT7Cho th (C)

10725)( 2 xxxfy . Tm trn

ng thng 24y cc im c th k ctip tuyn n (C)

6) - tip tuyn ca hm siu vitBT1

Cho th (C) ).43()( 2 xexxfy v gcto O(0;0) .Vit phng trnh tip tuyn iqua im O(0;0) n th (C)

BT2( H Xy Dng 2001)

Cho th (C) ln.)( xxxfy v M(2;1)T im M k c bao nhiu tip tuyn n

th (C)

BT3

Cho th (C)x

lnx1

y Vt phng trnh

tip tuyn i qua 0(0;0) n (C)

Chng 5

tnh li ,lm v imun ca th

1)- xc nh tnh li ,lm v imun ca th

BT1

Xc nh cc khong li, lm v im un ca th (C)

1) 1752 23 xxxy

2) 162 22 xxy

3) 762010 235 xxxxy

4) 0)(a3 22

3

ax

xy

5) 3 31 xy

BT2

Xc nh cc khong li, lm v im un ca th (C)

1) )(0;trongcot.2sin

cos3

gxx

xy

2) xexy ).1( 2

3)x

xy

ln1

ln

4) )7ln12.(4 xxy

5) 3 2 1 xy

2)-tm K than s (C): y=f(x) nhn i(m,n)lm im un

BT1

Tm a,b (C) 223 xbxaxy c imun I(1;-1)

BT2

Tm m (C) 13 23 m

xxy c im un I(-

1; 3)

BT3

Tm a,b (C) 02 byaxyx c im un

25;2I

BT5

Cho hm s (C)b)0a())(()( bxaxxxfy

Tm a,b im un ca th nm trnng cong 3xy

BT6

Tm m th (C)

1).12(38 234 xmmxxy C 2 im unc honh tho mn bt phng trnh

045

2

2

2

xx

xx

3)-chng minh th c 3 im un thnghng , vit phng trnh ng thng

BT1

Chng minh rng cc th sau c 3 im un

thng h

ng ,.Vit ph

ng trnh

ng thng iqua 3 im un

1)1

122

xx

xy


15/36



2)12

x

mxy

3)33

322

2

xx

xxy

4)2

322

2

x

xxy

5)1

32

2

xxxy

6)2

122

2

xx

xxy

Chng 6

tim cn ca ng cong1)-tm cn hm phn thc hu t

BT1(H Y Dc TPHCM 1997)

Cho (C)

0)#a,1-#(a2

3).12(2

x

axaaxy

CMR tim cn xin ca (C) lun i qua 1im c nh

BT2(H Xy Dng 2000)

Tm cc ng tim cn ca th hm s

12

2.32

2

xx

xxy

BT3Tm cc ng tim cn ca cc hm s

1

42

2

mxx

xy

32

22

mxx

xy

)1(

13

2

mxmx

xy

12

652

2

mxx

xxy

BT4

Tm m 2

32

mmxx

xy

ch c ng

mt tim cn ng

BT5

Tm m 1

12

mxx

xy c 2 tim cn

ng l x=x1 v x=x2 sao cho

35

5

3

2

3

1

21

xx

xx

BT6

Cho (C)2

1sin.2cos.2

x

axaxy

1)Xc nh tim cn xin ca th trn

2)Tm a khong cch t gc to n timcn xin t Max

BT7

Cho (C) )2(2)1()(

232

mx

mmmxxmxfy

vi m # -1 .CMR ttim cn xin ca (C) luntip xc vi mt Parabol c nh

BT8

Cho (C)1

232)(

2

x

xxxfy

CMR tch cc khong cch t M thuc (C) n 2

tim cn lun khng iTm M thuc (C) tng cc khong cch t Mthuc (C) n 2 tim cn nh nht

BT9(HSP TPHCM 2001 Khi D )

Cho (C)1

12)(

2

x

xxxfy

CMR tch cc khong cch t M thuc (C) n2 tim cn lun khng i

BT10(HSP TPHCM 2001 Khi A )

Cho (Cm)1

22)(2

xmxxxfy

Tm m ng thng tim cn xin to vi 2trc mt tam gic c din tch bng 4


Cho (C)1

22)(

2

x

xxxfy

Tm M thuc (C) sao cho khong cch t Mn giao im ca 2 ng thng tim cn l nh

nhtBT12

Cho (Cm)

0)#(m2).1(

)(222

mx

mmxmmmxxfy

CMR khong cch t gc to n tim cnxin khng ln hn 2

2)-tm cn hm v t v hm siu vitBT1

Tm tim cn ca cc th hm s sau

1) 74235)( 2 xxxxfy


16/36



2) 32132

1)( 2

xxx

xxfy

3) mtheo9

)(2

2

xm

xxfy

4) mtheo32

1)(

2

mxx

xxfy

5) mtheo42

4)(

2

2

mxx

xxfy

6) mtheo14

)(2

mx

mxxxxfy

BT2

Tm m hm s sau c tim cn ngang

7443)( 2 xxmxxfy

BT3Tm tim cn ca cc th hm s sau

1)cos

3)(x

xxxfy

2) xexy .2

3) xx

xy 2

ln 2

4)2

1

. xexy

5) )1ln(.x

exy

Chng 7

Kho st v v th hm s1)-kho st hm s bc ba

BT1

Kho st v v cc th hm s sau

1) 132 23 xxy

2) 533 23 xxxy

3) 863 23 xxxy

4)3

1

3

2 23 xxy

5) 133 23 xxxy

6) 433

1 23

xxxy

7)

333

)2()1( xxxy

BT2(H M 1997)

Cho (Cm) 53)2( 23 mxxxmy

Kho st khi m=0

Tm m hm s c C,CT

BT3(H M 1998)

Cho (C) xxxy 96 23

1) Kho st v v th (C)

2) Tm m (d) : y= m x ct (C) ti 3 im phnbit O,A,B . CMR trung im I nm trn 1

ng thng song song vi OyBT4(HGTVT 1994 )

Cho (C) xxy 43

1 3


2) Tm k : 0)2.(3

)1.(44

3

1 23

k

kxx c 3

nghim phn bit

BT5(HGTVT 1996 )

Cho (C) 4923 xmxxy 1) Kho st v v th (C) khi m=6

2) Tm m (C) c mt cp im i xngnhau qua gc to

BT6(HV BCVT TPHCM 1998 )

Cho (C) 12123 xxy


2)Tm cc im M thuc ng thng y= -4 k

c 3 tip tuyn n (C)BT7(HV NH HN 1998 )

Cho (C) xxy 33


2)S dng th tm Max,Min caxxy

3sin33sin

BT8(HNTHN 1998 )

Cho (Cm) mmxmmxxy 3).1(333223

1)

Kho st v

v th khi m=02) CMR : hm s (Cm ) lun c C, CT nm trn2 ng thng c nh

BT9(H NT HN 2000 )

Cho (C) 196 23 xxxy


2)T M bt k thuc ng thng x=2 k cbao nhiu tip tuyn n (C)

BT10(HKTHN 1996 )

Cho (Cm))32)(1(2).772( 223 mmxmmmxxy

1) Kho st v v th khi m= -1

2)Tm m hm s ng bin trn [2; +)


17/36



3)Tm m th tip xc vi trc honh

BT11(HKTHN 1998 )

Cho (C) 393 23 xxxy


2) CMR trong s cc tip tuyn ca (C) th tiptuyn ti im un c h s gc nh nht

BT12(HNNHN 1998 )Cho (Cm ) 2)12(

3

1 23 mxmmxxy

1) Kho st v v th m= 2

2) T

3

4;

9

4A k c my tip tuyn n (C2)

3)Tm m hm s nghch bin trn (-2;0)

BT13(HTCKT 1996 )

1)Vit phng trnh ng thng i qua C,CTca (Cm ) 37

23 xmxxy


3)Tm m (Cm ) c cp im i xng qua O

BT14(HTCKT 1998 )

Cho (Cm )1)1(6)12(32 23 xmmxmxy


2)Tm im c nh

3)Tm m (Cm ) c C,CT .Tm qu tch CBT15(H An Ninh 1998 )

Cho (C ) xxy 33

Kho st v v th (C)

Vit phng trnh Parabol i qua 0;3A ,0;3B v tip xc vi (C)

BT16(H An Ninh 1999 )

Cho (Cm ) 4)32(3223 xmmmxxy

1) Kho st v v th m=12)Vit phng trnh Parabol i qua C,CT ca

(C1 ) v tip xc y= -2x+2

3)Tm m (Cm ) c C,CT nm v 2 pha caOy

BT17(H Lm Nghip 1999 )

Cho (C ) xxy 3

1) Kho st v v (C)

2)Tm m (C) ct (d) : y=-3x+m ti 3 imphn bit

3)Gi (C) giaom(d) ti x1, x2, x3 Tnh2

3

2

2

2

1 xxxS

BT18(HSPHN 2000 )

Cho (Cm ) )(423

xfmxxy

Kho st v v th m= 3

Tm m f(x)=0 c ng mt nghim

BT19(HQGHN 2000 )

Cho (Cm ) mmxxxy 23 3

1) Kho st v v th m=02) Tm m hm s nghch bin trn nt on

c di bng mt

BT20(HSP2 HN 1999 )

Cho (C ) 233 xxy

Kho st v v th (C)

Tm trn Ox nhng im k c 3 tip tuyn ti(C)

BT21(H Thi Nguyn 1999 )Cho (C )

3

2

3

1 3 xxy

1) Kho st v v th

2)Vit phng trnh (P) i qua C,CTv tip xc

vi ng thng3

4y . Tm qu tch cc

im k c 2 tip tuyn vung gc vi nhaun (P)

BT22(HQGTPHCM 1998)

Cho (C ) xxy 33

Kho st v v th

Tm m phng trnh1

23

2

3

m

mxx c 3

nghim phn bit

BT23(HQGTPHCM 1999)

Cho (C ) 3223 )1(33 mxmmxxy

1) Kho st v v th m= -2

2)Tm m (C) ct Ox ti 321 0 xxx

BT24(HV Ngn hng TPHCM 2001)

Cho (C ) 1)1(6)12(32 23 xmmxmxy

Kho st v v th m=1

CMR xC- xCTkhng ph thuc vo m

BT25(Bo Ch 2001)

Cho (Cm ) 53)2(23 mxxxmy

1) Kho st v v th m=0

2)Tm m hm s c C,CT

3) CMR T A(1;-4) k c 3 tip tuyn n C0

BT26(H Hu 2001)


18/36



Cho (Cm )323

2

1

2

3mmxxy

Kho st v v th m= 1

Tm m hm s c C,CT i xng qua y=x

Tm m y= x ct )(mC ti A,B,C phn bit sao

cho AB=BC

2)-kho st h

m trng ph

ngBT1

1)Kho st v v (C)2

53

2

24

xx

y

2)Ly M thuc (C) vvi xM=a .CMR honh giao im ca tip tuyn (d) ti M vi (C) lnghim 0)632.( 222 aaxxax

3)Tm a (d) ct (C) ti P,Q khc M .Tm qutch trung im K ca PQ

BT2(H Kin trc HN 1999)Cho )( mC

)21()1()( 24 mxmmxxfy

Tm m hm s c 1 im cc tr

Kho st v v th khi2

1m

Vit phng trnh tip tuyn ca th cu (2)bit tip tuyn i qua O(0;0)

BT3(H M a Cht 1996)

Cho )(mC

1)12()( 234 mxxmmxxxfy

1)Kho st v v th khi m = 0

2)Tm m f(x)> 0 vi mi x

BT4(Hkin Trc TPHCM 1991)

Cho )( mC

1)12()( 234 mxxmmxxxfy

Kho st v v th khi m = 0

Tm A thuc Oy k c 3 tip tuyn n th cu (1)

Tm m phng trnh f(x)=0 c 2 nghim khcnhau v ln hn 1

BT5(HV QHQT 1997)

Cho )(mC

424 22)( mmmxxxfy

1)Kho st v v th khi m = 1

2)Tm m hm s c cc C,CT lp thnh

tam gic uBT6(H Nng 1997)

Cho )( mC 5)(24 mmxxxfy

Tm cc im c nh ca h ng cong )( mC

vi mi m

Kho st v v th vi m=- 2

Vit phng trnh tip tuyn vi th ti imc honh x=2

BT7(HQG HN 1995)

Cho (C)22

)1()1( xxy Kho st v v th (C)

Bin lun s nghim phng trnh0222 24 bxx

Tm a (P) : 32 axy tip xc vi (C) Vitphng trnh tip tuyn chung ti tip im

BT8(HSP HN2 1997)

Cho )( mC

12)1()( 24 mmxxmxfy

1)Tm m )( mC ct Ox ti 4 im phn bit

2)Tm m hm s c cc tr

3)Kho st v v th vi m= 2

BT9(H Nng 1999)

Kho st v v th 56)( 24 xxxfy

Cho M thuc (C) vi xM =a Tm a tip tuynti M ct (C) ti 2 im phn bit khc M

BT10(HNN 1999)

1)Kho st v v th4

92

4

1)( 24 xxxfy

2) Vit phng trnh tip tuyn ca th tigiao im ca n vi Ox

BT11(H M a Cht 1999)

Kho st v v th 4223)( xxxfy

Bin lun theo m s nghim ca phng trnh2424 22 mmxx

BT12(H M a Cht 1999)1)Kho st v v th

(C) 45)( 24 xxxfy

2)Tm m (C) chn trn ng thng y=m baon thng bng nhau

3) Tm m ng thng y=m ct (C) ti 4 imphn bit

BT13(H Cnh st 2000)

Cho (Cm )2

3

2

1 24 mxxy

Kho st v v th m= 3


19/36



Vit phng trnh tip tuyn i qua

2

3;0A dn

(C) ( cu 1)

Tm m hm s c CT m khng c C

BT14(H Thu L 2001)

Cho (Cm ) mxxy 24 4

1) Kho st v v th m= 32)Gi s )( mC ct Ox ti 4 im phn bit .Tm

m hnh phng gii hn bi )(mC vi Ox c

din tch phn pha trn v din tch phn phadi Ox bng nhau

BT15(H Ngoi Thng TPHCM 2001)

Cho (Cm ) 9)10(224 xmxy

Kho st v v th m= 0

CMR vi mi m # 0 )(m

C ct Ox ti 4 im phn

bit . CMR trong s cc giao im c 2im thuc (-3;3) v 2 im khng thuc(-3;3)

3)-kho st hm a thc bc bnBT1

Kho st v v th 34 34 xxy

Vit phng trnh ng thng (D) tip xc vi(C) ti 2 im phn bit , tm honh tip

im x1, x2Gi (D) l ng thng song song (D) v tipxc (C) ti im A c honh x3, v ct (C)ti B,C .CMR : 2132 xxx v A l trung

im BC

Bin lun theo m s nghim phng trnh084 34 mxxx

BT2 (HBK TPHCM 1998)

Kho st v v th4522 234 xxxy

Vit phng trnh ng thng (D) tip xc vi(C) ti 2 im phn bit

Bin lun theo m s nghim phng

04

1322 234 mxxxx

BT3

1)Kho st v v th 234 34

3xxxy

2) Bin lun theo m s nghim phng

034

3 234 mxxx

BT4 (HM a Cht 2000

Cho phng trnh :0)36(51172 234 kxkxxx

CMR phng trnh c nghim khng ph thucvo k

Bin lun theo k s nghim phng trnh

BT5 Cho hm s )( mC :234 4 mxxxy

Kho st v v th vi m= 4

Tm m 104 234 xmxxx

4)-kho st hm phn thc bc 1/bc 1BT1

1)Kho st v v th (C)

2

12

x

xy

2) CMR ng thng y= -x+m lun ct (C) ti 2im A,B phn bit . Tm m di onAB nh nht

3)Tm m phng trnh : mx

x

2sin

1sin.2c

ng 2 nghim x thuc [0; ]

BT2

Cho )( mC mx

mxmy

)1(

Vi m=1 :

Kho st v v th (C)

Tm m thuc (C) tng cc khong cch tM bs 2 tim cn nh nht

2) CMR mi m # 0 th )( mC lun tip xc vi

mt ng thng c nh


1)Kho st v v th (C)1

12

x

xy

2) Ly M thuc (C) vi x M = m . tip tuyn ca(C) ti M ct cc tim cn ti A,B . Gi I lgiao im ca cc tim cn . CMR : M ltrung im ca AB v din tch tam gic IABkhng i mi M

BT4 (HQG HN (D)1997)

Kho st v v th (C)3

13

x

xy

Tm Max(y) , Min(y) khi 0

x

2BT5 (H Thi Nguyn (D)1997)


23

x

xy


20/36



2) Tm trn (C) cc im c to nguyn

3)CMR: Khng tn ti im no thuc (C) tip tuyn ti i qua giao im ca 2ng tim cn

BT6 (H cnh St 1997)

Kho st v v th (C)2

23

x

xy

Vit phng trnh tip tuyn c h s gc bng 4. Tm to tip im

BT7 (HQGHN 1998)


1

x

xy

2) Tm trn Oy cc im k c ng 1 tiptuyn n (C)

BT8 (H Dc 1998)

Kho st v v th (C) 212

x

xy

Tnh din tch hnh phng gii hn bi (C), Oxv ng thng x=1

Tm m phng trnh mx

x

2sin

1sin2c ng 2

nghim thuc [0; ]BT9 (HVQHQT 1999)

1)Kho st v v th (C)

3

2

x

xy

2) Tm M thuc (C) khong cch t M ntin cn ng bng khong cch t M ntim cn ngang ca (C)

BT10 (H Ngoi Thng TPHCM 1999)

Kho st v v th (C)2

2

x

xy

Tm M thuc (C) cch u 2 trc to Ox, Oy

Vit phng trnh tip tuyn i qua A(-6; 5) n

(C)BT11 (CSP TPHCM 1998)


1

x

xy

2) CMR (d) : 2x- y + m =0 lun ct (C) ti A,Bphn bit trn 2 nhnh

3)Tm m di on AB nh nht

BT12 (C Nng 1998)

Cho hm s )( mC 1

1

mx

mmxy

Kho st v v th (C) vi m=2

Tm M thuc (C) ( cu 1) tng khong ccht M n 2 tim cn l NN

CMR mi m # 1, th )(mC lun tip xc vi

1 ng thng c nh

BT13 (H SPTPHCM 2001)

Kho st v v th (C)1

2

x

xy

Cho im A(0; a). Tm a t A k c 2 tip

tuyn n (C) sao cho 2 tip im t

ng ngnm v 2 pha i vi trc Ox

BT14 (C Hi Quan 2000)

Cho hm s )( mC mx

mxy

1

1)Kho st v v th (C) vi m=2

2) Tm m hm s lun ng bin hoc hm slun nghch bin trn tng khong xc nh

3)Tm im c nh ca )( mC

BT15 (H Qui Nhn 2000)

Cho hm s )( mC )(2

22 2

mx

mmmxy

Kho st v v th (C) vi m=1

CMR )( mC khng c cc tr

Tm trn Oxy cc im c ng 1 ng ca h)(

mC i qua

5)-kho st hm phn thc bc 2/bc 1

BT1


632

x

xxy

2)Tm 2 im M,N thuc (C) i xng nhau quaA(3; 0 )

BT2

Kho st v v th (C)2

522

x

xxy

Tm M thuc (C) tng khong cch t M n2 tim cn l NN

BT3 (HXD 1993)

1)Kho st v v th (C))1(

332

x

xxy

2)CMR in tch 2 tam gic to bi 2 tim cn 2tm cn v tip tuyn bt k l khng i

BT4 (HXD 1994)

Cho )( mC mx

mxmxy

2

Kho st v v th vi m= 1.Vit phng trnhtip tuyn i qua A(-1; 0 ) n th

Tm m hm s khng c cc tr


21/36



BT5 (H Kin Trc HN 1995)

Cho )(mC

1

12

x

mxxy

1)Tm im c nh ca ng cong

2)Tm m hm s c C,CT

3)Kho st v v th hm s khi m=0

4)Bin lun s nghim phng trnh kx

x 112


Cho )( mC 0#m2

2)1(2

x

mxmmxy

Tm m tim cn xin ca th vung gc vi(d) : x + 2y -1 =0

Kho st v

v th vi m tm

cTm k (d) qua A(0; 2) vi h s gc k ct th (2) ti 2 im khc nhau ca ng cong


Kho st v v (C)1

12 2

x

xxy . m nhng

im thuc Oy t k c 2 tip tuynvung gc vi th

BT8 (HHH 1999)

Kho st v v th (C)1

12

xxxy

1)Tm im thuc (C) cch u 2 trc to

2)Tm m y = m x ct (C) ti 2 im phnbit CMR 2 giao im thuc 1 nhnh ca (C)

BT9 (HHH Tp HCM 1999)

Cho (C)1

2

x

xy

1)Kho st v v th hm s

2) Tm A,B thuc (C) i xng nhau qua ngthng y= x - 1

BT10 (HGT 1999)

Cho (C)3)1(2 2

ax

xaxy

Kho st v v th hm s vi a= 2

Tm a tim cn xin ca th (1) tip xc(P) y= x2 + 5

Tm qu tch giao im ca tim cn xin v timcn ng ca (C)

BT11 (HGT TPHCM 1999)

Cho )( mC 1

123)(

2

x

mmxmxxfy

1)Tm m th )( mC c TCX i qua A(1; 5)

2) Kho st v v th hm s vi (C1) vi m=1

3) Tm m d f(x) > 0 vi mi x thuc [4; 5]

BT12 (HVBCVT HN 1997)

Cho (C)1

1)(

2

x

xxxfy

Kho st v v th hm s

Tm M thuc (C) tip tuyn ti M giao , Oyti A,B tam gic OAB vung cn

BT13 (HVBCVT HN 2000)

1) Kho st v v th hm s1

12

x

xxy

2) Vit phng trnh tip tuyn ca th hms , bit tip tuyn song song vi (d) : y= - x

BT14 (HV Ngn Hng 2000)

Cho )(mC

1)1( 22

mx

xmxmy

Kho st v v th hm s khi m =1

Tm A thuc (d) : x= 2 sao ch th )( mC khng

qua A vi mi m


Cho )(mC

4)1( 322

mx

mmxmmxy

1) Tm m hm s c 1 im cc tr thuc gcphn t (II) mt im cc tr thuc gc phnt (IV)

2) Kho st v v th hm s khi m = - 1

3) Tm trn mi nhnh ca th (2) mt im khong cch gia chng l nh nht

BT16 (HKTQD HN 1995)

Cho )(mC

4)1( 322

mx

mmxmmxy

Kho st v v th hm s khi m = 1

CMR mi m # -1. )(mC tip xc vi mt ng

thng c nh

Tm m hm s trn ng bin (1; + )


Cho )( mC 1

122

x

mmxxy

1) Kho st v v th hm s khi m = 1 . Binlun s nghim ca phng trnh

0112 xkxx


22/36



2) Tm m C,CT ca )( mC nm v 2 pha ca

Ox


Kho st v v th hm s2

32

x

xxy

Tm k y= kx + 1 ct (C) ti A,B Tm qutch trung im I ca AB

BT19 (HVQHQT 1996)


422

x

xxy

2) CMR mi tip tuyn ca th u khngi qua giao im ca 2 ng tim cn


Cho )( mC 2422

x

mmxx

y

Tm im c ssnh ca h )( mC

Tm m hm s c C,CT . Tm qu tch imC

Kho st v v th hm s khi m = - 1


Cho )( mC 1)1(2

mx

mxmxy

1) Kho st v v th hm s vi m= 22) Tnh cc khong cch t 1 im bt k ca

(C) cu (1) ti 2 tim cn l hng s

3) Tm m hm s c C,CT v yC. yCT> 0

BT22 (HQG HN 2001)


2

x

xy

2) Tm trn (d) : y= 4 cc im t c th kc 2 tip tuyn ti th v gc gia 2

tip tuyn bng 450BT23 (HSPHN 2001)

Cho )(mC

1

222

x

mxxy

Kho st v v th hm s vi m= 1

Tm m hm s c C,CT v khong cch t 2im n ng thng x + y + 2 = 0 l nhnhau

BT24 (HSP II HN 2001)

1) Kho st v v th (C)1

12

x

xxy

2) Tm A thuc (C) khong cch t A n2 tim cn l Min

BT25 (HBK HN 2001)

Kho st v v th (C)1

32

x

xy

Vit phng trnh (d) i qua

5

2;2M sao cho

(C) ct (d) ti A,B v M l trung im AB

BT26 (H Ngoi thng 2001)

Kho st v v th (C)1

222

x

xxy

Tm im M trn th hm s khongcch t M n giao im ca 2 ng timcn l Min

BT27 (H TCKT HN 2001)

Cho )( mC )2(2)1( 232

mx

mmmxxmy

1) Kho st v v th hm s khi m = 0

2) Tm m hm s )( mC lun nghch bin trn

TX ca n

BT28 (HTM HN 2001)

Kho st v v th (C)2

52

x

xxy

CMR : tch cc khong cch t 1 im M bt kthuc (C) n cc tim cn l hng s

Tm trn mi nhnh ca (C) mt im khongcch gia chng l Min

BT28 (H An ninh 2001)


22

x

xxy

2) Tm A thuc (C) tip tuyn ca th ti

A vung gc vi ng thng i qua A v quatm i xng ca th

BT29 (HVKTQS 2001)

Kho st v v th )( mC

1

1)2(2

x

mxmxy khi m=2

Tm m trn th c A,B phn bit tho mn :;035;035

BBAA yxyx v A, Bi xng qua (d) : x+ 5y +9 = 0

BT30 (HVQY 2001)

1) Tm m 2

)6(2 2

mx

xmxy c C, CT


23/36



2) Kho st v v th hm s khi m= 1 . CMRti mi im thuc th tip tuyn lun ct2 tim cn ti 1 tam gic c din tch khngi

BT31 (H SPKT TPHCM 2001)

Cho )( mC 1

22 2

x

mxxy

Tm m tam gic to bi 2 trc to v TCXca th c din tch bng 4

Kho st v v th hm s khi m = - 3

BT32 (H Y Dc TPHCM 2001)

Cho )(mC

4)1( 322

mx

mmxmmxy

1) Kho st v v th hm s khi m = - 1

2) Tm m )( mC c 1 im cc tr thuc gc

phn t th (II) v 1 im cc tr thuc gcphn t th (IV)

BT32 (H D Nng 2001)

Kho st v v th (C)12

x

xxy

Tm m phng trnh :01)1(3)1( 234 tmttmt c nghim

BT33 (HTCKTHN 1997)

Cho )( mC 132 2

x

mxx

y


2) Bin lun theo m s nghim phng trnh

0alog1

232

2

1

2

x

xx

3) Tm m hm s ng bin trn (3;+ ) Fgf

BT34 (HTCKTHN 1999)

Cho )( mC

22

mx

mmxx

y


2) Tm m hm s c C,CT . Vit phngtrnh ng thng i qua C,CT

3) Tm cc im c ng 2 ng thng ca h)(

mC i qua

BT35 (HTCKTHN 2000)

Cho (C)1

222

x

xxy

Kho st v v th hm s

Tm cc im trn (C) tip tuyn ti d vunggc vi TCX ca th

BT36 (HV QY 2000)

Cho )(mC

22

mx

mmxxy


2) Tm nhng im thuc Oy t c th kc 2 tip tuyn ti th cu (1) vunggc vi mhau

3) Vit phng trnh ng thng qua C,CT

BT37 (HV KTQS 2000)


542

x

xxy

2) Tm cc im thuc (C) c khong cch n(d) : y+ 3x + 6 =0 l Min

BT38 (H An Ninh 1997)

Cho (C))1( 22

mx

mxmy

Kho st v v th hm s m= 1

CMR vi mi m # 0 TCX ca th hm s luntip xc vi mt (P) c nh


Cho (C)1

2

x

xy

1) Kho st v v th hm s

2) Vit phng trnh (P) i qua C,CT ca (C)v tip xc vi (d) :

2

1y

4) Tm A,B thuc 2 nhnh khc nhau ca (C)sao ch AB min


Cho (C)1

82

x

mmxxy

Kho st v v th hm s khi m= -1

Vit phng trnh (P) i qua C,CT ca (C) vtip xc vi (d) : 2x y 10 =0

Tm m C, CT ca )(mC nm v 2 pha ca

9x 7y -1 =0BT41 (H Cng on 2000)


1

xxy

2) Tm m y= m giao vi ti A, B sao choOA,OB vung gc vi nhau

BT42 (H Lm Nghip 2000)

Kho st v v th (C)1

12

x

xxy


24/36



Tm trn mi nhnh cu (C) khong cch giachng l Min

Vit phng trnh (P) i qua C,CT ca (C) vtip xc vi y= - 1

BT43 (HSPHN II 2000)

Cho )( mC )1(

244)1( 22

mx

mmxmxy


2) Tm m hm s xc nh v ng bin trn( 0; + )

BT44 (HQG HN 1999)

Cho )( mC 1

24)1( 22

x

mmxmxy

Kho st v v th hm s khi m =0

Tm m hm s c cc tr , tm m tch cc

C v CT dt MinBT45 (HSPHN II 1998)

Cho )( mC 1

2

mx

mxmxy

1) Tm m )( mC ng bin trn ( 0; + )


3) Ly M bt k thuc )( mC . Bin lun s tip

tuyn qua M

BT46 (CSPHN 2000)Cho )(

mC 1

3)1(32

x

mxmxy

Kho st v v th hm s khi m= 0 . Tm k y= kx +2 ct (C) ti 2 im phn bit nmtrn 2 nhnh ca (C)

T A thuc )(mC k AP,AQ ln lt vung gc

vi cc TCX, TC ca )( mC .CMR din tch

tam gic APQ l hng s


Cho )(mC

1

)1()2(2 222

mx

mxmxmy

1) Kho st v v th hm s khi m=-2

2) CMR vi mi m # 0 )( mC lun c C,CT

3) CMR vi mi m # 0 , TCX ca )( mC lun

tip xc vi (P) c nh . Tm phng trnhca (P)

BT48 (HSP Vinh 1998)Cho )( mC

2

mmx

mmxxy

vi m # 0

Kho st v v th hm s khi m= 1

Tm im c nh ca h )(mC

Vit phng trnh ng thng i qua

4

5;0M

v tip xc (C) cu (1)

BT49 (HSP Qui Nhn 1999)

Cho )(m

C 1

2)1(22

x

xmxy

1) Kho st v v th hm s khi m=0 CMRgiao ca 2 tim cn l tm i xng ca (C) .Tm a (C) tip xc vi (P) : y= - x 2 + a

2) Tm m hm s ng bin trn ( 0; + )

BT50 (H Lt 2000)

Cho (C)1

122

x

xxy

Kho st v v th hm s

Tm m phng trnh01cos)2(cos2 mtmt c nghim

BT51 (H Y Dc TPHCM 1999)

Cho (C)12

x

xy


2) Tm M t M k c 2 tip tuyn n (C)vung gc vi nhau

BT52 (H Y D

c TPHCM 2000)Cho )( mC

1)1(2 2

mx

mxmxy

Kho st v v th hm s m = 1

CMR vi mi m # - 1. )(mC tip xc vi mt

ng thng c nh ti mt im c nh .Tm phng trnh ng thng c nh

BT53 (H Ngoi Thng TP HCM 1996)

Cho (C) 122

x

xx

y 1) Kho st v v th hm s

2) Tm A thuc Ox qua A ch k c 1 tiptuyn duy nht ti (C)

BT54 (HSP TP HCM 2000)

Cho (C)1

222

x

xxy

Kho st v v th hm s

Gi I l

tm i xng ca (C) , M thuc (C) . tiptuyn ti M ct TC,TCX ti A,B .CMR :MA=MB v din tch tam gic IAB l hng s

BT55 (HQG TP HCM 2000)


25/36



Cho (C)1

12

x

xxy


2) Tm M thuc (C) khong cch t M n 2tim cn c tng Min

BT56 (H Cng Nghip TP HCM 2000)

Cho (C)1)2(

2

xxy

Kho st v v th hm s

ng thng (d) qua I(-1;0) c h s gc k .Bin lun theo k s giao im ca (d) v (C)

Gi M thuc (C) . CMR tch khong cch t Mn 2 ng tim cn l hng s

BT57 (H Cn Th 2001)

Cho (C)132

x

xxy


2) Tm trn ng thng x= 1 cc im M kn (C) hai tip tuyn vung gc vi nhau

BT58 (H Kinh T TPHCM 2001)

Cho (C)2

962

x

xxy

Kho st v v th hm s

Tm trn ng thng Oy cc im M k c

tip tuyn n (C) v song song vi ng

thng xy4

3

4)-kho st hm cha gi tr tuyt iBT1 (HBK TPhCM 1993)

Cho (C)2

922

x

xxy


2)

Bin lun theo m s nghim m ca ph

ngtrnh 22)-m.(x

2

922

x

xx

BT2

Cho (C)12

562

x

xxy

Kho st v v th hm s

Bin lun theo m s nghim m ca phngtrnh mxxx 2

2 log.1256

BT3 (HXD 1997)

Cho )(mC

12)2( 22

mx

mxmmxy

1) Kho st v v th hm s khi m = -1 . T

suy ra th1

12

x

xxy

2) Tm m hm s c cc tr vi m )( mC

lun tm c 2 im m tip tuyn vi thti 2 im vung gc vi nhau

BT4 (H Kin Trc Hn 1995)Cho )( mC

1

12

x

mxxy

Tm im c nh ca h )(mC

Tm m hm s c C,CT

Kho st v v th hm s khi m = 0

Bin lun theo m s nghim phng trnh

k1

12

x

x

BT5 (H GTVTHN 1998)

Cho (C)1

22

x

xxy


2) T v th1

22

x

xxy

BT6 (HV Ngn Hng 2000)

Cho (C)1

552

xxxy

Kho st v v th hm s

T v th1

552

x

xxy .Bin lun theo

m s nghim phng trnh)12(52.54 ttt m

BT7 (H Thng Mi HN 1995)

Cho (C)1

122

xmmxxy

1) Kho st v v th hm s vi m = 1..Binlun theo m s nghim phng trnh

0112 xkxx

2) Tm m C,CT nm 2 pha ca Ox

BT9 (H M Hn 1999)

Cho (C)1

11

xxy


2) T v th1

11

xxy


26/36



3) Tm m phng trnh c 3 nghim phn bit

m1

11

xx

BT10 (Phn Vin BCHN 2000)

Cho (C)222

mx

mmxxy

Kho st v

v th h

m s khi m= 1T v th

1

322

x

xxy

Tm m hm s ng bin trn (1;+ )

BT11 (HSPHN II 2000)

Cho (C)12

562

x

xxy


2)

Bin lun theo m s nghim m ca ph

ngtrnh 1256x 2 xkx


Cho (C)1

632

x

xxy

Kho st v v th hm s (C) . t nu cch

v th (C)1

632

x

xxy

T O c rth k c bao nhiu tip tuyn vi (C). Tm to cc tip im (nu c )

BT13 (H BKTPHCM 1995)

Cho (C)1

12

x

xxy

1) Kho st v v th hm s .T v th

1

12

x

xxy

2) Tm m phng trnh sau c nghim

01)1(2

mxmx 3) Tm m phng trnh sau c 3 nghim

phn bit thuc [-3;0]01)2)(1()2( 222 mttmtt

BT14 (H Thu Li 1998)

Cho (C) )23(3

1 23xaaxx

ay

Tm a hm s lun ng bin

Tm a th ct Ox ti 3 im phn bit

Kho st v v th hm s2

3a . T v

th2

5

2

3

6

1 23xxxy

BT15 (H Hu 1998)

Cho (C) 2)1(3 23 xmmxxy

1) Tm m hm t CT ti x=2 . Kho st v v th hm s khi


1

222

x

kxx


Cho (C) 33 xxy

Kho st v v th hm s (C) v t suy ra

th hm s : 33

xxy

Tm m phng trnh sau c 3 nghim phn

bit1

23

2

3

m

mxx

BT17 (H GTVT TPHCM 2000)Cho (C) 23 cbxaxxy

1) Tm a,b,c th c tm i xng l I(0,1)v t cc tr ti x=1

2) Kho st v v th hm s khi a =0,b=-3,c=1 .Bin lun theo m s nghim phng

trnh 0k33

xx

BT18 (HSPHN 2001)

Cho (C) xxxy 96 23

Kho st v v th hm s


0m3-96 23

xxx

BT19 (H Vn Lang TPHCM 2001)

Cho (C)2

842

x

xxy

1) Kho st v v th hm s (C) .

2) T nu cch v th (C)

2

842

x

xxy

BT20 (H Y Thi bnh 2001)

Cho (C)2

922

x

xxy

Kho st v v th hm s

Bin lun theo k s nghim m phng trnh

22)-k(x2

922

x

xx

5)-kho st Phn Thc bc hai / bc haiBT1


27/36



Cho (C)3

322

2

x

xxy

Kho st v v th hm s


m3

322

2

x

xx(*)

1)

Gi s ph

ng trnh (*) c 2 nghim x1, x2Tm h thc lin h gia 2 nghim khngph thuc m

BT2

Cho (C))1(2

2322

2

x

xxy


2) CMR tip tuyn ti 2 giao im ca (C) viOx l vung gc vi nhau

BT3

Cho (C)122

12

xx

xy

Kho st v v th hm s

CMR (C) c 3 im un thng hng

BT4

Cho (C))1( 2

x

xy

1)

Kho st v

v th h

m s2) Gi s ng thng y =m ct th (C) ti 2im M,N phn bit . Tm qu tch trung imI ca MN

3) Gi A,B,C l 3 im phn bit thuc (C),CMR nu A,B,C thng hng th

2.. CBACBA xxxxxx

BT5

Cho (C)2

2

2

xx

xy

Kho st v v th hm s

Tm m y= m.x ct (C) ti 3 im phn bit

Bin lun theo m s nghim phng trnh02)1( 24 mmxxm

BT6

Cho (C)452

xx

xy


2) Gi A,B l 2 im cc tr , th Ab ct th (C) ti C . Tm to C

3) Tip tuyn ti C ct (C) ti D Tm to D

BT7

Cho )( mC 6)25(2

4622

2

xmx

mxxy

Tm cc im c nh ca h )(mC

Gi (C) l th ca )( mC khi th )( mC ct

tim cn ngang ti im c honh bng2

3

. Kho st v v th hm s (C)Vit phng trnh tip tuyn k t O n th

(C)

CMR (C) c 3 im un thng hng . Vitphng trnh ng thng i qua 3 im un

BT8 (H Hng Hi 1997)

Cho )(mC

1cos2

cos2cos.2

2

axx

axaxy vi a

thuc (0; )1) Kho st v v th hm s

3

a

2) CMR | F(x) | 1 vi a thuc (0; )Chng 8

Khai thc ng dng ca th v tnh cht hm s

1)-Bin lun phng trnh bng thBT1

Cho (C)1

12

x

xxy

Kho st v v th hm s

Bin lun theo m s nghim

2;

2

x ca

phng trnh 01sin)1(sin 2 mxmx

BT2

Cho (C)1

12 2

x

xxy


2) Bin lun theo m s nghim

2;

2

x ca

phng trnh 01sin)1(sin2 2 mxmx

BT3

Cho (C)2

12

x

xy

Kho st v v th hm s


28/36



Tm m phng trnh sau c ng 2 nghim

;0x :2sin

1sin2m

x

x

BT4

Tm m phng trnh sau

1) mxxxx 58102 22 c 4 nghim

phn bit2) 22 285232 xxmxx c nghim duy

nht

3) 0)2(1 mxx c 3 nghim phn bit

4) mxxx 652 Bin lun theo m s nghim

5) 052 xmxx c 4 nghim phn bit

6) mxx 2)1( 2 c 4 nghim phn bit

BT5

Kho st v v th hm s 342 xxy


mmxxx 342

BT6

1) Kho st v v th hm s 322 xxy


mmxxx

32

2

BT7

Kho st v v th hm s xxxy 23 2

Bin lun theo m s nghim phng trnh02 23 mxx

2)-Bin lun bt phng trnhbng th

BT1

Tm m bt phng trnhmxxxx 2)6)(4( 2 ng vi mi x

thuc [ - 4 ; 6]

BT2

Cho BPT 321)2( 2 xxmxx

1) Tm m BPT c nghim

2) Tm m di min nghim ca BPT bng2

BT3

Tm m bt phng trnh182)2)(4(4 2 mxxxx ng vi

mi x thuc [ -2 ; 4]

BT4

Cho BPT 26)6( 2 mxxxx .Tm m

BPT c di min nghim p tho mn

2 p 4

BT5

Cho (C)1

122

x

xxy

Kho st v v th hm sTm a nh nht 222 )1()1( xxxxa

nghim ng 1;0x

3)-Bin lun H phng trnhbng th

BT1

Tm a h

4)(

)1(2

2

22

yx

ayxc ng 2

nghimBT2(H Thng Mi 2000)

Cho h phng trnh

0

0

22xyx

aayx

1) Tm a h c ng 2 nghim phn bit

2) Gi );();;( 2211 yxyx l nghim ca h CMR :

1)()( 2122

12 yyxx . Du bng xy rakhi no

BT3(HVQHQT 1996)

Cho h phng trnh

ayx

ayx

3

21

Tm a h c nghim

BT4

Cho h phng trnh

ayx

axyyx

22

Tm a h c nghim

BT5


mxx 22 sin.21cos.21

4)-Bin lun H bt phng trnhbng th

BT1

Cho h Bt phng trnh

064

02

2

2

axx

axx

Tm a h BPT c nghim

Tm a h BPT c nghim duy nht

BT2(H Ngoi Thng 1996)


29/36



Tm m h bt phng trnh c nghim

01886

042

24

2

mxxx

mxx

BT3(H Giao Thng 2001)

Tm m h c nghim

2)1(2

2

ayxyx

yx

BT4

Tm m h c nghim duy

nht

myx

myx

22

22

)1(

)1(

BT5

Tm m h c nghim 0;0 yx

02084

93

22

22myxyx

yx

yx

BT6

Tm m h

0)1(

0232

32

2

mxmmx

xx

1) C nghim

2) C nghim duy nht

BT7Tm m h

024)25(

4

22

22

mmxmx

mx

C nghim

C nghim duy nht

BT8

Tm m h

043

02

2

2

mxx

mxx

1) C nghim2) C nghim duy nht

Chng 9

Mt s dng ton khc1)-S tng giao hm bc ba

BT1

Cho )( mC

)12(2)232()1(

223 mmxmmxmxy Tm m )(

mC ct Ox ti 2 im phn bit

BT2

Cho )(mC )(44)(

23mmxxmmxy

Tm m )(mC tip xc vi Ox

BT3

Cho )(mC

232)1(4)14(2 2223 mmxmmxmxy

Tm m )(mC ct Ox ti 3 im phn bit

3214

1xxx

BT4

Cho )(mC

)5(2)75()21(2 23 mxmxmxy


1321 xxx

BT5

Cho )( mC

)1()12(2 2223 mmxmmxxy


321 1 xxx

BT6

Cho )(mC

)1(4)45(2)65( 223 mmxmmxmxy


3211 xxx

BT7

Cho )(mC mxxy

232

Tm m )(mC ct Ox ti 3 im phn bit c

honh 321 ,, xxx v

tnh : 232

2

2

1 xxxS

BT8

Cho )( mC 233323

mxmxxy Tm m )(

mC ct Ox ti 3 im phn bit c

honh 321 ,, xxx sao cho2

3

2

2

2

1 xxxS t

GTNN

BT9( HVCNBCVT 2001)

Cho (D) 2)1( xmy v (C) xxy 33

Tm m (D) ct (C) ti 3 im phn bitA,B,C trong A l im c nh v tip

tuyn vi th ti B,C vvung gc vi nhauBT10

Cho )(mC 1)(

23 mxxxfy


30/36



CMR phng trnh f(x) = 0 lun c 1 nghimdng

Tm m )(mC ct Ox ti ng 1 im

BT11(HBK 1999)

Cho )(mC 2

23 mxxy

Tm m )(mC ct Ox ti ng 1 im

BT12

Tm m 023 mxx c nghim 2;0x

BT13(HQGTPHCM 1998)

Tm m 1

23

2

3

m

mxx c 3 nghim phn

bit

BT14( HQGHN _D 1998)

Cho )( mC mxxxy 9323

Tm m )(

mC ct Ox ti 3 im phn bit

2)-phng trnh bc ba c 3 nghimlp thnh CSC,CSN

BT1

Cho )( mC mxxxy 9323

Tm m )(mC ct Ox ti 3 im phn bit lp

thnh CSC

BT2

Cho )(mC

323 43 mmxxy

Tm m )( mC ct ng thng y = x ti 3

im phn bit lp thnh CSC

BT4(H M HN 2000)

Cho )(mC xxmxy 9)12(

23


thnh CSC

BT5

Cho )(mC

12)1()1( 23 mxmxmxy


thnh CSC

BT6

Cho )( mC

12)1()1( 23 mxmxmxy


thnh CSN

BT7

Cho )( mC 216)34(4)15(823 xmxmxy

Tm m )( mC ct Ox ti 3 im phn bit lp

thnh CSN

BT8

Cho )(mC mmxxxmy 47218)3(

323


thnh CSN

BT9

Cho )(mC 1929)22(3

23 mxxmxy


thnh CSN

BT10(H Y HN 2000)

Cho (C) 132 23 xxy Tm a,b (C) ct(D) :y= ax + b ti 3 im phn bit A,B,C sao

cho AB = BCBT11

Cho (C) 193 23 xxxy Tm a,b (C) ct(D) :y= ax + b ti 3 im phn bit A,B,C saocho AB = BC

3)-phng trnh bc bn c 4 nghimlp thnh CSC,CSN

BT1

Cho )( mC 124 mmxxy Tm m )( mC ct Ox ti 4 im phn bit lp

thnh CSC

BT2

Cho )(mC 122

24 mmxxy


lp thnh CSC

BT3

Cho )(mC

mxmxxy 3)1(2 24 Tm m )(

mC ct Ox ti 4 im phn bit lp

thnh CSC

BT4(H Hu 2000)

Cho (C) 45 24 xxy

Tm m ng thng y = m ct (C) tiA,B,C,D phn bit m AB=BC=CD

4)- S t

ng giao h

m hu tBT1(H Cng on 1998)


31/36



Tm m (Dm) y= mx + 2 m ct th

(C)2

142

x

xxy ti 2 im phn bit thuc

cng mt nhnh ca (C)

BT2(CSP TPHCM 1998)

CMR ng thng (D) 2x y + m = 0

lun ct th (C) 11

x

x

y ti 2 im phnbit A,B thuc 2 nhnh ca (C)

BT3(H Cn Th 1998)

CMR ng thng (D) y =2x + m lun ct

th (C)1

33

xxy ti 2 im phn

bit A,B c honh x1 ,x2 . Tm m sao cho 221 xxd nh nht

BT4(H Thu Sn 2000)

Cho th (C)1

12

x

xxy tm k

(D) : 2 kkxy ct (C) ti 2 im phn bit

BT5

Cho th (C)1

3)12(2

x

xmmxy tm

m (D) : 23 xy ct (C) ti 2 im phnbit thuc 2 nhnh ca (C)

BT6(HBK HN 2001)Vit phng trnh ng thng (D) i qua

5

2;2M sao cho (D) ct th (C):

1

32

x

xy

ti phn bit v M l trung im ABBT7(H Y Thi Bnh 2001)

Tm m ng thng (D) 10)5( xmy

ct th (C):2

922

x

xxy ti phn bit v

M(5;10) l trung im ABBT8(HQGHN 2001B)

CMR vi mi m ng thng y= m lun ct

th (C) :1

12

x

xxy ti A,B phn bit .

Tm m di AB nh nht

BT9 (HSPKT TPHCM 2001)

Cho )(mC :

1

22 2

x

mxxy Tm m tam

gic to bi 2 trc to v TCX ca )( mC cdi tch bng 4

BT10 (H Duy Tn 2001)

Tm m )(mC :

2

1)3(2

x

xmmxy ct

Ox ti A,B phn bit sao cho di AB nh nht

5)- Tm i xng v tnh i xngqua 1 im

BT1(H TCKTHN 1996)

Tm m )( mC 3723 xmxxy c mtcp im i xng nhau qua gc to

BT2(H Thu Li 1999)

Tm m trn)( mC

2223 1)1(33 mxmmxxy c hai

im i xng nhau qua gc to

BT3

Tm trn (C) :

24

53

x

xy cc im i xng

nhau qua I(1;-2)BT4

Tm trn (C) :1

152 2

x

xxy cc im i

xng nhau qua I(-2 ; -5)BT5

Tm trn (C) :1

12

x

xxy . Tm th (C):

y=g(x) i xng vi th (C) qua im I(2 ;1)BT6

Tm trn (C) :1

12

x

xxy . Tm th (C):

y=g(x) i xng vi th (C) qua im I(2 ;1)

BT7

Cho )(mC : 21

)1)((

x

mxmxy

. CMR hai

th )(mC v (C - m ) i xng nhau qua O(0;0)

BT8

CMR th (C) :1

222

2

x

xxy . Khng c

tm i xngBT9

Tm trn (C) :5

723 2

x

xxy . cc im i

xng nhau qua I(1,3)BT10

Tm trn (C) :12

954 2

x

xxy . cc im i

xng nhau qua I(3,2)


32/36



6)- Trc i xng v tnh i xngqua ng thng

BT1

CMR (C) : 286865243 234 xxxxy ctrc i xng

BT2

Tm m )( mC c trc i xng

201250)1( 234 mxxxmxy

BT2

Cho )(mC

39)8(352)12( 234 xmxxmxy

Tm m )(mC c trc i xng

BT3

CMR (C) : 3108 715122

2

xx

xxy c trc i

xngBT4

1)CMR (C) :12

53

x

xy c 2 trc i xng

2)CMR (C) :24

95

x

xy c 2 trc i xng

BT5

CMR (C) :2

1322

xxxy c 2 trc i xng

CMR (C) :12

1043 2

x

xxy c 2 trc i xng

BT6

Cho th (C) :1

352 2

x

xxy .Vit phng

trnh th (C) i xng vi (C) qua ngthng y= - 1

BT8

Cho th (C) :23

174 2

x

xxy .Vit

phng trnh th (C) i xng vi (C) quang thng x=1

7)- bin lun s thi qua mt im

1) im c nh ca h th

BT1Tm im c nh ca h ng cong sau

)(mC )1(4)14(2)1(3

223 mmxmmxmxy

BT2

CMR )( mC

18712)246()4( 23 mmxxmxmy lun c 3im c nh thng hng . Vit phng trnhng thng i qua 3 im

BT3 (HQG TPHCM D 1999)

Tm im c nh m h th hm s )( mC

1)2()1(23

mxmxmmxy lun i quavi mi m

BT4

1)CMR )( mC 1)12()1(23 mxmxmy lun

c 3 im c nh thng hng

2) Vi gi tr no ca m th )( mC c tip tuyn

vung gc vi ng thng qua 3 im

BT5 (H Nng 1997)

Tm im c nh ca h ng cong sau

)(mC 5

24 mmxxy

BT6 (H AN Ninh 2000)

Cho hm s )( mC 123 mmxxy ,. Vit

phng trnh tip tuyn ti cc im c nh mh ng cong lun i qua vi mi m

BT7 (H Ngi 1997)

Tm im c nh h

)(m

C2

422

x

mmxxy

BT8 (H Hu 1996)

Tm im c nh h

)(mC

mx

xmxy

)1(4

4)4(3 2

BT9

CMR th hm s

)(mC

mx

xmxy

3)1(2 2khng i qua im

c nh noBT10

CMR th hm s

)(mC

mxm

mxy

4)2(

13

lun i qua 2 im c

nh2)im c mt vi th i qua

BT1

Cho h th )( mC mx

mxmy

22

)1(

CMR: Cc im nm bn phi trc tung lunc ng 2 th ca h )(

mC i qua


33/36



BT2Cho h th )(

mC 2)1(3 mxmy v

im A(a;b) cho trc . Bin lun s ng congca h )( mC i qua A

BT3Cho h th )(

mC 1224 mmxxy

CMR : vi mi im A(a;1) thuc ng y= 1lun c ng mt th ca )(

mC i qua

BT4Cho h th )(

mC

1325 223 mmxmxxy CMR khng tnti im A(a;b) sao cho c 3 th phn bit cah )(

mC i qua

BT5Bin lun s ng cong c h )( mC

mxmxxy

2

2

i qua im A(a;b) cho trc

BT6Cho )(

mC 0422.2 mxmmxmyxy

1) Tm cc im M sao cho c ng mt thca )(

mC i qua

2) Tm cc im M sao cho c ng hai thca )(

mC i qua

BT7Cho h th )(

m

C mxmxy 4)1( 223

Tm M thuc ng x= 2 sao choQua im M(2;y) c ng mt th ca )(

mC i

quaQua im M(2;y) c ng hai th ca )(

mC i

quaQua im M(2;y) c ng ba th ca )(

mC i

qua

3)im khng c th no ca

h th i quaBT1

Cho h th (Pm) 12 22 mmmxxy .Tm cc im thuc Oxy m khng c th noca (Pm) i quaBT2

Cho h )(mC 2)(

232 mxmxxfy .

Tm cc im thuc Oxy m khng c th noca )(

mC i qua

BT3Cho h )( mC

4532)( 2323 mmmxxxfy . Tm cc

im thuc Oxy m khng c th no ca)(

mC i qua

BT4

Cho h )(mD

1.

1

12

2

2

mm

mx

mm

my

Tm cc im thuc Oxy m khng c th noca )(

mD i qua

BT5

Cho h )( mC 1)22()( 2 mxmmxxfy . Tm cc

im thuc Oxy m khng c th no ca)( mC i qua

BT6

Cho h )(mC

mx

mmxxy

222. Tm cc


mC i qua

BT7

Cho h )(mC

52

422

2

xx

mmxxy . Tm cc

im thuc Oxy m khng c th no ca)( mC i qua

BT8

Cho h )( mC 1

3)1(2

mxmxmy . Tm cc


mC i qua

BT9

Cho h )(mC

mx

xmxmy

1)1( 22. Tm

trn ng thng x=2 nhng im khng c)(

mC no i qua

8)- bi ton s tip xc 2 th1) iu kin tip xc ca 2 th ( K

nghim bi , nghim kp )

BT1

1) Tm m )( mC mxmxxy 3323 tip

xc vi Ox

2) Tm m )( mC

)12(2)232()1( 223 mmxmmxmxy

tip xc vi ng thng y = -49x+98

3) Tm m )( mC 616323 mxmxy tip

xc vi Ox


34/36



4) Tm m (C) xxxy 44 23 tip xc vi

)( mD y =mx 3m +3

5) Tm m (C) mxxmxxy 234 )1( tip xc vi Ox

6) Tm m (C) 42)5( 24 mmxxmxy tip xc vi Ox

BT2Tm m

24)21(33:)(

2)21(:)(

3

2

23

1

mxmmxyC

mxxmmxyC

tip xc vi nhau

BT3

Tm m )(mC

mmx

mxxmy

4)2)(1( 2.

Tip xc vi y= 1BT4

Tm m )(mC

mx

mmxmxmxy

)3()13()12( 223. Tip

xc vi ng thng y= x + m + 1

BT5

Tm m TCX ca

1

2)12(2

x

mxmmxy . Tip xc vi

(P) 92 xy

BT6

Vit phng trnh tip tuyn chung

3:)(

23:)(

2

2

2

1

xxyP

xxyP

BT7

Cho (P) 622 xxy v (C)x

xy

12 CMR

c ng 2 tip tuyn chung tip xc vi (C) v(P)

2) iu kin tip xc ca 2 th

( K o hm )BT1

Tm M

)( mC 818)3(3223 mxxmxy Tip xc

vi Ox

BT2Tm m

110102:)(

214126:)(

23

2

2234

1

xxxyC

mmxxxxyC

tip xc vi nhauBT3

Tm m

mxyC

x

xx

yC

1:)(

1

1

:)(2

2

2

1 tip xc vi nhau

BT4

Vit phng trnh tip tuyn chung

103)(:)(

65)(:)(

3

2

xxxgyC

xxxfyP

BT5

CMR (C) xx

xfy ln)( lun tip xc vi y=e 3) H ng cong tip xc vi ng c nh

BT1

CMR h )(mC

mx

mmxmy

2)13(. lun

tip xc vi 2 ng thng c nhBT2

CMR vi mi m #-1, TCX ca )(mC

mx

mmmxxmy

)2(2)1(

232

. lun tip

xc vi 1Parabol c nhBT3

CMR h )( mC

4

3534

22345 m

mxxxxxy

. lun

tip xc vi 1 ng cong c nhBT3( H An ninh 1997)

CMR TCX ca )(mC

(m#0))1( 22

mx

mxmy

. lun tip xc vi

1Parabol c nhBT4

CMR TCX ca )(mC

(m#0)162)2()54( 2322

mx

mmxmmxmy

. lun tip xc vi 1Parabol c nhBT5

CMR TCX ca )(mC


35/36



(m#0)cos

)sincos.(sincos. 22

mx

mmmxmxy

lun tip xc vi 1Parabol c nhBT4

CMR )(mC

(m#0)1

4)2()12( 223

x

mxmmxmxy

lun tip xc vi 1 ng cong c nh

BT5

CMR )(mC

(m#0)3m-)1(33 3223 mxmmxxy .un tip xc vi 2 ng thng c nh

4) Bi ton v tip tuyn ,tip xc khng

dng phng php nghim kp

(phng php o hm )BT1

Vit phng trnh tip tuyn i qua im

A(1;1 ) n (C)2

542

x

xxy

BT2

Vit phng trnh tip tuyn tip xc vi

th (C)4

522 234 xxxy . Ti 2 im phn

bitBT3

CMR vi mi m # -1 h th

)(mC

mx

mxmxy

1)1(2 2lun tip xc

vi nt ng thng c nh

9)- im c to nguyn trn th

BT1 (HQG HN 1999)

Tm M thuc (C) 2 12

x

xxy c to l

cc s nguyn

BT2 (H Thu Sn 1999)

Tm M thuc (C)1

41

xxy c to l

cc s nguynBT3

Tm M thuc (C)

12

38

x

xy c to l cc

s nguynBT4

Tm M thuc (C)23

410

x

xy c to l cc

s nguynBT5

Tm M thuc (C)1

862

x

xy c to l cc

s nguynBT6

Tm M thuc (C)1

3122

xx

xy c to l

cc s nguyn

10)- tm tp hp im

BT1

Tm qu tch nh (P)1)34(2 22 mxmxy

BT2Cho (Dm) y= mx+2 v (Pm) 32 mxxy

Tm m (Dm) ct (Pm) ti 2 im phn bitA,B .Tm qu tch trung im I ca AB

BT3(H QGTPHCM 1998)

Cho (C) 23 3xxy v (D):y=mx .Tm m (D) ct (C) ti 3 im phn bit A,O,B .Tm qutch trung im I ca ABBT4(H M a Cht 1998)

Cho (C) xxxy 96 23 v (D):y=mx .Tmm (D) ct (C) ti 3 im phn bit A,O,B.Tm qu tch trung im I ca ABBT5(H Thng Mi 1999)

Cho (D) 2x - y + m = 0 v (C)1

42

x

xy

.Tm m (D) ct (C) ti 2 im phn bit M,N

.Tm qu tch trung im I ca MNBT6(H Hu 1997)

Cho (Dm) y = mx -1 v (C)1

12

x

xxy

.Tm m (D) ct (C) ti 2 im phn bit M,N

.Tm qu tch trung im I ca MNBT7(H Ngoi Thng 1998)

Tm qu tch C,CT ca

mmxmmxxy 3)1(33 3223

BT8( H Ngoi ng 1997)

Tm qu tch C,CT ca

)(mC

2

422

x

mmxxy

BT9( H Nng 2000)


36/36


Tm qu tch C,CT ca

)(mC

1

12

x

mmxxy

BT10

CMR trn mt phng Oxy c ng 1 imva l C va l CT vi 2 gi tr m khc nhau

ca h )( mC mx mxmmxy

1)1(

32

BT11(H Duy Tn 2000)

Tm qu tch C,CT ca mmxxy 233

BT12

Tm qu tch tm i xng ca

)(mC

mx

mmxmy

)42()2( 2

BT13 (H Hu 1996)

Tm qu tch tm i xng ca

)(mC

mx

xmxy

)1(4

4)4(3 2

BT14

Tm qu tch tm i xng ca )(mC

mx

mmxmmxmy

2

22)2(2)1(4 22

BT15

Tm qu tch tm i xng ca )(mC

1)3(2)1(2 23 mxmxmmxy

11)- khong cch

BT1

Cho )(mC

1

7sin.4cos.3 2

x

mxmxy Tm m

khong cch t O(0;0) n TCX t Max

BT2Cho (C)

12

74

x

xy Tm M thuc (C) tng

cc khong cch t M n 2 tim cn ca (C) lnh nht

BT3

Cho (C)23

85

x

xy Tm M thuc (C) tng

cc khong cch t M n 2 trc to Ox, Oyl nh nht

BT4

Cho (C)34

52

x

xy Tm trn mi nhnh ca

(C) cc im M1 ,M2 sao cho 21MM l nh nht

BT5( H Ngoi Thng 1998)

Cho (C)1

12

x

xxy Tm trn mi nhnh ca

(C) cc im M1 ,M2 sao cho 21MM l nh nhtBT6

Cho (C)1

532 2

x

xxy Tm M thuc (C)

khong cch t M n Ox gp 3 ln khong ccht M n Oy

BT7

Cho (C)52

1874 2

x

xxy Tm M thuc (C)

tng cc khong cch t M n 2 tim cn ca(C) l nh nht

BT9 (H SPHN2 2001)

Tm )();( 11 CyxA 1

12

x

xxy vi x1>1

sao cho khong cch t A n giao im ca 2tim cn l nh nht

BT10

1)Cho (C) 12

173 2

x

xxy Tm trn mi nhnh

ca (C) cc im M1 ,M2 sao cho 21MM l nh

nht

2)Cho )(mC

2

11cos.5sin.4 2

x

mxmxy Tm m

khong cch t A(-1;0) n TCX t Max

bai toan lien quan kshs qua de thi dai hoc

Documents