lt cap toc toan btvn va huong dan giai chuyen de khao sat ham so 2541

8/2/2019 Lt Cap Toc Toan Btvn Va Huong Dan Giai Chuyen de Khao Sat Ham So 2541

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P.2512 34T Hong o Thy Tel: (094)-2222-408

H Ni, ngy 12 thng 06 nm 2010

BI TP V NH

(Chuyn kho st hm s) Cu I : Cho hm s

12 1 x

y x

+= + (C)

I.1 . Vit phng trnh tip tuyn i qua im M(2 ; 3) n (C)I.2 . Vit phng trnh tip tuyn vi (C), bit rng tip tuyn i qua giao im ca 2ng tim cn.I.3 . Vit phng trnh tip tuyn ti im ( ) M C , bit tip tuyn ct 2 trc ta t thnh 1 tam gic c din tch bng 1.I.4 . Vit phng trnh tip tuyn ti im ( ) M C , bit tip tuyn ct 2 trc ta t thnh 1 tam gic cn.

Cu II : Cho hm s ( )1m x m y x m

+= ( )mC

II.1 . CMR th hm s lun tip xc vi mt ng thng c nh ti 1 im c n

II.2 . Tip tuyn ti ( )m M C ct 2 tim cn ti A, B. CMR M l trung im ca ABII.3 . Cho im ( )0 0M x , y ( )3C . Tip tuyn ca( )3C ti M ct cc tim cn ca (C) ti cc im A v B. Chng minh din tch tam gic AIB khng i, I l giao ca 2 tim cnTm M chu vi tam gic AIB nh nht.

Cu III:

Cho hm s2 22 1 3 x mx m y

x m+ + =

. Tm tham s m hm s c:

1. Hai im cc tr nm v hai pha trc tung.2. Hai im cc tr cng vi gc ta O lp thnh tam gic vung ti O3. Hai im cc tr cng vi im M(0; 2) thng hng.4. Khong cch hai im cc tr bng10m .

5. Cc tr v tnh khong cch t im cc tiu n TCX.6. Cc tr v tha mn: 2 3CD CT y y+ > .

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Cu IV : Cho hm s1

2 1 x

y x +

= + (C)

Tm m (C) ct ng thng( ): 2 1md y mx m= + ti 2 im phn bit A, B:a. Thuc 2 nhnh ca th (C)b. Tip tuyn ti A, B vung gc vi nhau

c. Tha mn iu kin4 . 5OAOB =

Cu V : Cho hm s ( )

2

3 32 1

x x y x

+ = (1)

a. Tm m ng thng y = m ct th hm s (1) ti A v B saAB=2

b. Tm m ng thng d: ( )2 3 y m x= + v ng cong (1) ct nhauti A, B phn bit sao cho M(2; 3) lm trung im ca AB.

Cu VI :

Cho hm s ( )1m x m y x m +=

( )mC

Da vo th hm s, ty theo m hy bin lun s nghim ca phtrnh:

a.2

2 31 log

3

xm

x

+ =

b.2 3

2 1 03

xm

x+ + =

Cu VII : Cho hm s ( )

2 3 32 1

x x y

x + = (1)

a. Tm trn th 2 im A, B thuc 2 nhnh sao cho AB min. b. Tnh din tch tam gic to bi tim cn xin v cc trc ta .

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Cu VIII : Cho hm s 12 1 x

y x

+= +(C)

a. Tm im M thuc (C) sao cho tng khong cch t M n 2 trcta t GTNN

b. Tm im M thuc (C) sao cho tng khong cch t M n 2 timcn t GTNN

c. Tm 2 im A; B thuc 2 nhnh ca th hm s sao cho AB min.

.HtBT Vin mn Ton hocmai.vn

Trnh Ho Quang

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HDG CC BTVNCu I : Cho hm s 1

2 1 x

y x

+= + (C)

I.1 . Vit phng trnh tip tuyn i qua im M(2 ; 3) n (C)I.2 . Vit phng trnh tip tuyn vi (C), bit rng tip tuyn i qua giao imng tim cn.I.3 . Vit phng trnh tip tuyn ti im ( ) M C , bit tip tuyn ct2 trc ta to

thnh 1 tam gic c din tch bng 1.I.4 . Vit phng trnh tip tuyn ti im ( ) M C , bit tip tuyn ct 2 trc ta t thnh 1 tam gic cn.

HDG

Tp xc nh: 1\2

D R = . Ta c: ( )2

3' 0,

2 1 y x D

x

= < +

Bi 1:

V ng thng x = 2 khng l tip tuyn ca (C), nn phng trnh ng thng M (2; 3) c h s gc k c dng: ( )2 3 y k x= + tip xc vi (C) khi v ch khi h:

( )

( )2

12 3

2 13

2 1

xk x

x

k x

+ = ++ =+

c nghim

Th k t pt th hai vo pt u ta c:

( )( ) 22

1 32 3 7 4 4 0

2 1 2 1

x x x x

x x

+ = + + + =+ + : V nghim

Vy khng c tip tuyn no i qua M n (C)Bi 2:

Hm s c: TC: 12 x= ; TCN:12

y = 1 1;2 2 I

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od/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915


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V ng thng 12

x = khng l tip tuyn ca (C), nn phng trnh ng thng i

1 1;

2 2 I

c h s gc k c dng: 1 12 2

y k x = + + tip xc vi (C) khi v ch khi h:

( )2

1 1 12 1 2 2

3

2 1

xk x

x

k x

+ = + + + =+

c nghim

Th k t pt th hai vo pt u ta c:

( ) ( )21 3 1 1 3 3

2 1 2 2 2 1 2 2 12 1

x x

x x x x

+ = + = + + + + :V nghim

Vy khng c tip tuyn no i qua I n (C)Bi 3:

Gi ( )00

1 3 1;

2 4 2 M x C

x

. Tip tuyn ti M c dng:

( )02 20 0 0 0

3 3 1 3 3 1:

4 4 2 4 2 2d y x x x

x x x x = + = +

Gi s Ox; A d B d Oy= = suy ra:( )0 0 0

0

2 3 3;0 ; 0;

3

x x x A B

x

OAB vung to O ( )201 2

. 3 12 3OAB

S OAOB x = = =

0 06 6 6

32 2

x x = =

Vy c 2 tip tuyn tha mn l: 3 4 62040 12 6

y x = +

hay 3 4 6

2040 12 6 y x

+= +

Bi 4:

Tip tuyn ct 2 trc ta to thnh mt tam gic cn nn h s gc ca tip tu 1k = . Gi ( ) ( )0 0; M x y C l tip im

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- Nu( )

0 02

0

3 1 31 1 2 1 3

22 1k x x

x

= = + = =+

Vi 0 01 3 1 3

2 2 x y

= = tip tuyn l: 1 3 y x=

Vi 0 01 3 1 3

2 2 x y

+ += = tip tuyn l: 1 3 y x= +

- Nu ( )( )202

0

31 1 2 1 3

2 1k x

x

= = + = + : V nghim

Vy c 2 tip tuyn tha mn bi ton l: 1 3 y x= v 1 3 y x= +

Cu II : Cho hm s ( )1m x m y x m

+= ( )mC

II.1 . CMR th hm s lun tip xc vi mt ng thng c nh ti 1 im c n II.2 . Tip tuyn ti ( )m M C ct 2 tim cn ti A, B. CMR M l trung im ca AB

II.3 . Cho im ( )0 0M x , y ( )3C . Tip tuyn ca( )3C ti M ct cc tim cn ca (C) ti cc im A v B. Chng minh din tch tam gic AIB khng i, I l giao ca 2 tim cnTm M chu vi tam gic AIB nh nht.

HDGBi 1:

Gi ( )0 0; M x y l im c nh ca hm s( ) 0

00

1;

m x m y m

x m

+ =

( ) ( )0 0 0 0 00 0 0

0 0 0 0

1 0;

1 0 0

0 1

m x y x x y m

x y x

x x y y

+ + + = + + = = + = =

Vi ( )0; 1 M , tip tuyn ti M l: ( )' 0 1 1 y y x x= =

Vy th hm s lun tip xc vi mt ng thng c nh 1 y x= ti ( )0; 1 M .

Bi 2:

Ta c:2

1m

y m x m

= + TC: x m= v TCN: 1 y m=

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7/16


P.2512 34T Hong o Thy Tel: (094)-2222-408


Gi ( )2

; 1 , 0mm

M a m m C aa

+ +

. Tip tuyn ti M c dng:

( ) ( ) ( )2 2 2

2: ' 1 1m m m

d y y a m x a m m x a m ma a a

= + + + = + +

Gi A, B l giao im ca ng thng d vi TCN, TC tng ng nn:

( )22

2 ; 1 ; ; 1m

A a m m B m ma

+ +

Nhn thy 22

A B M

A B M

x x x y y y

+ =+ = M l trung im ca AB (pcm)

Bi 3:

im ( )39 9

: 2 3 ;23

M C y M x

= + + +

Phng trnh tip tuyn ca M c dng: 2 29 18 27

: 2 y x

= + + +

Gi A, B l giao im ca ng thng d vi TCN, TC tng ng nn:

( ) 182 3; 2 ; 3;2 A Ba

+ + V I l giao im ca 2 tim cn nn( )3;2 I

+ IAB vung ti I nn: 1 1 18. . . 2 . 182 2 IAB

S IA IB

= = = (vdt)

+ Chu vi tam gic IAB l:

2

218 182 4 p IA IB AB

= + + = + + +

2

218 182 2 2 4 12 2.2.18 12 6 2

+ + = + = +

Du = xy ra 182 3

= = ( )6;5 M hoc ( )0; 1 M

Cu III:

HDG:

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od/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915http://hocmai.vn/mod/resource/view.php?id=24915


8/16


P.2512 34T Hong o Thy Tel: (094)-2222-408


Tp xc nh: { }\ D R m=

Ta c:( ) ( )

2 2

2 21 1 2 13 ' 1 x xm m y x m y

x m x m x m + = + + = =

1:

Hm s c hai im cc tr nm v hai pha trc tungy = 0 c 2 nghim tri du2 2( ) 2 1 g x x xm m = + c 2 nghim tri du cng khc m

2 1 01 1

( ) 0

mm

g m

< < + = +

Du = xy ra khi0 00

3 3 3 1 3 1;

4 2 2 2 x x M

x

= =

Vy 3 1 3 1;2 2 M

th min 3 1d =

b. . Khong cch t M n TCN, TC ln lt l:1 0d x= ; 20

34d x=

Page 15 of 16


16/16


P.2512 34T Hong o Thy Tel: (094)-2222-408


1 2 0 0

0 0

3 32 . 3

4 4d d d x x

x x= + = + = , du = xy ra khi0

3

2

x =

Kt lun: 3 1 3 1;2 2 M

hoc 3 1 3 1;2 2 M

l cc im cn tm

c . Gi 1 3 1;2 4 2 A a a

thuc nhnh tri, 1 3 1;2 4 2 B b b

thuc nhnh phi

ca th hm s (C), vi 0a b< < . Ta c:

( ) ( ) ( )22

22 3 3 3 3 324 4 4 4 2

b a AB b a b a

b a b a ab

= + = 3 4. 62

abab

=

Du bng xy ra( )

22

32

3 33

4 42

b a a

b abb a

= = = =

Vy hai im cn tm l: 3 1 3 1;2 2 A ; 3 1 3 1;2 2 B th min 6 AB =

.Ht BT Vin mn Ton hocmai.vn

Trnh Ho Quang

lt cap toc toan btvn va huong dan giai chuyen de khao sat ham so 2541

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