Persamaan Ellips yang Berpusat di P (g, h) By :

1.Kharisma Ayu H.2.Waidatin Nur A.

Matematika Peminatan IRISAN KERUCUT (ELLIPS)SMA N 1 SRAGEN

Persamaan Ellips dengan pusat P (g, h)

1)()(2

2

2

2

bhy

agx

y

x0

A2 A1 F2 F1

a

b

P (g, h)

Direktriks Direktriks

B2

B1

Matematika Peminatan IRISAN KERUCUT (ELLIPS)SMA N 1 SRAGEN

Persamaan Ellips dengan pusat P (g, h)

Direktriks y

x0

A2

A1

F2

F1

P (g, h)B2 B1

Direktriks

1)()(2

2

2

2

ahy

bgx

Matematika Peminatan IRISAN KERUCUT (ELLIPS)SMA N 1 SRAGEN

b

a

Perbandingan

Matematika Peminatan IRISAN KERUCUT (ELLIPS)SMA N 1 SRAGEN

Graph the following Ellipse

19)3(

25)2( 22

yx Center: (2, -3)

a = 5 in x direction

b = 3 in y direction

Contoh Soal :

Graph the following Ellipse

19)3(

25)2( 22

yx

a = 5 b = 3 a2 = b2 + c2

52 = 32 + c2

25 = 9 + c2

16 = c2

4 = c

Graph the following Ellipse

19)3(

25)2( 22

yx

a = 5 b = 3 c = 4 abLR22

518

LR

Find the Length of the LR. 532 2

LR

Graph the following Ellipse

19)3(

25)2( 22

yx

Center: (2, -3)Major Axis: length = 10 endpoints (-3, -3) & (7, -3)Minor Axis: length = 6 endpoints (2, 0) & (2, -6)Foci: (-2, -3) (6, -3)

Length of LR: 518

Exercise

1324

)5(4324

)2(9 22

yx

9x2 + 36x + 4y2 - 40y - 100 = 88(9x2 + 36x ) + (4y2 - 40y ) = 88 + 100

9(x2 + 4x + 22) + 4(y2 - 10y + (-5)2) = 188 + 36 + 100

9(x + 2)2 + 4(y - 5)2 = 324

181)5(

36)2( 22

yx

Exercise 1

81)5(

36)2( 22

yx

Center: (-2, 5)a = 9 in y directionb = 6 in x direction

Graph the following Ellipse

a = 9 b = 6 a2 = b2 + c2

92 = 62 + c2

81 = 36 + c2

45 = c2

c53)535,2(

)535,2(

181)5(

36)2( 22

yx

53

53

Graph the following Ellipse1

81)5(

36)2( 22

yx

abLR22

8LR

Find theLength of the LR.

a = 9 b = 6 c = 53

962 2

LR

Graph the following Ellipse

)535,2(

)535,2(

181)5(

36)2( 22

yx

Center: (-2, 5)

Major Axis: length = 18 endpoints (-2, 14) & (-2, -4)

Minor Axis: length = 12 endpoints (-8, 5) & (4, 5)

Foci: )535,2(

Length of LR: 8