# tugas terstruktur 4 (p arabolas , circles , and ellipses )

of 20 /20
Tugas Terstruktur 4 (Parabolas, Circles, and Ellipses) Presented by: Kelompok 4 1. Ihda Mardiana H. 2. Hesti Setyoningsih 3. Dewi Kurniyati 4. Belynda Surya F.

Post on 21-Mar-2016

34 views

Category:

## Documents

DESCRIPTION

Presented by: Kelompok 4 Ihda Mardiana H. Hesti Setyoningsih Dewi Kurni y ati Belynda Surya F. Tugas Terstruktur 4 (P arabolas , Circles , and Ellipses ). No 37 hal 52. Given the function defined by find the equation defining and graph and on the same set of axes - PowerPoint PPT Presentation

TRANSCRIPT

Tugas Terstruktur 4 (Parabolas, Circles,

and Ellipses)

Presented by:Kelompok 41. Ihda Mardiana H.2. Hesti Setyoningsih3. Dewi Kurniyati4. Belynda Surya F.

No 37 hal 52Given the function defined by find the equation defining and graph and on the same set of axesDiketahui: y= x2, (x ≥ 0)Ditanya: f -1 dan sketsa grafik f dan f -1 pada sumbu yang sama.Penyelesaian:Jelas

yx

yx

xy

1

2

2

xf 1

Sketsa grafiknya

𝑓

𝑓 −1

𝑌

𝑋

No 39 hal 53If and are two points on the parabola show that the line has the intercept .Solution:Jika dan merupakan titik-titik pada parabola, maka dan .Persamaan garisnya yaitu dimana

)()(

)(y-0

122112

1121121112

112

121

yyxyxyxyxyxyyxyxyx

xxxxyy

Untuk perpotongan terhadap sumbu x, , dan kita peroleh:

xpyy

yyxp

yyyy

yyxp

yyyy

yyxypyy

py

2

)(2

)(

)(2

)()(2

)(2

21

121221

122

21

221

122

21

1

22

No 10 hal 58Find the standart equation of the ellips having its center at the origin and meeting the given conditions. One vertex at (0,6) and containing (Solution:Vertexnya (0,6) berarti a=6Karena vertexnya terletak pada sumbu y maka focinya juga terletak pada sumbu y. Jadi, kita digunakan teorema 2.6

16b483b

43

b12

411b

12

1369

b12

136y

bx

1ay

bx

2

2

2

2

2

2

2

2

2

2

2

2

no 13 hal 58Find the standart equation of the ellips having its center at the origin and meeting the given conditions. One focus at (-4,0) and containing ( Answer:Salah satu fokus adalah (-4,0) berarti c=4Jarak fokus terhadap titik (3,1) adalah:

2 11)(

14)(3 yc)(x d

2

22

221

2550 1(7)

14)(3 yc)(x d

2

22

222

sehingga:

18a 23a 2

252a

2dda

2

21

21

12y

18x 22

2b 1618b

c-ab

2

2

222

No 14 hal 58Find the standart equation of the ellips having its center at the origin and meeting the given conditions. Length of major axis 12, length of minor axis 8, and foci on the y axisSolution:

Panjang sumbu mayor = 12 maka a = 6Panjang sumbu minor = 8 maka b = 4

Karena fokusnya terletak pada sumbu y, maka digunakan teorema 2.6

mayor sumbu panjang21a

minor sumbu panjang 2b

1

136y

16x

1ay

bx

22

2

2

2

2

No 15 hal 58Find the coordinates of the foci and vertices of the ellipse with the equation , and sketch the curve.Solution:Persamaan diatas memenuhi teorema 2.5 dengan a=4 dan b=2Diperoleh

Jadi, vertexnya (-4,0) dan (4,0) dan focinya ( dan )

32c12c

4c16bca

2

2

222

( 0,2 )

( -4,0 ) ( 4,0 )

( 0,-2 )

( 0,0 ) F2()F1()

No 21 hal 59Find the coordinates of the foci and vertices of the ellipse with the equation, and sketch the curve Solution:Jelas Dari persamaan di atas diperoleh a=4 dan b=2

Jadi, vertexnya (0,-4) dan (0,4) dan focinya ( dan

32c12c

4c16bca

2

2

222

X

Y

(0,4)

(-2,0)

(0,-4)

(2,0)

F1()

F2()

( 0,0 )

No 23 hal 59Find the eccentricity of the ellipse obtained in problem 15 : Answer:

Diperoleh dan 32c

12c4c16

bca

2

2

222

No 31 hal 59Find an equation of an ellipse with the foci at (0,3) and (0,-3) if Answer:Diketahui: foci= (0,3) dan (0,-3), berarti c=3, dan Sehingga

16bb925

bca

2

2

222

No 32 hal 59Find an equation of the ellipse that contains the point and has foci at (4,0) and (-4,0) Solution:Jarak fokus terhadap titik (3,-12/5) yaitu:

513

25169

251441)(

5124)(3

yc)(x d

2

22

22 1

537

251369

2514449

25144(7)

5124)(3

yc)(x d

2

22

22 2

5a253713

a

2dda

21

Karena focinya pada sumbu x maka kita menggunakan teorema 2.5Jadi, persamaan bakunya

9b 1625b

c-ab

2

2

222

Focinya (4,0) and (-4,0), berarti c=4, sehingga

No 40 hal 53Find an equation of the line containing the line segment with endpoints on the parabola that bisected by the point (4,2)

TERIMA KASIH… ^_^