The document defines and provides examples of ellipses. An ellipse is defined by the equation (x-g)^2/a^2 + (y-h)^2/b^2 = 1, where (g,h) is the center and a and b are the lengths of the semi-major and semi-minor axes. Examples are given of graphing ellipses and finding properties such as focal length and length of the major and minor axes. Exercises are also included for the student to practice graphing ellipses and determining related properties.

1. 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

2. Persamaan Ellips dengan pusat P (g, h)
1
)()(
2
2
2
2




b
hy
a
gx
y
x0
A2 A1F2 F1
a
b
P (g, h)
Direktriks Direktriks
B2
B1
Matematika Peminatan
IRISAN KERUCUT (ELLIPS)
SMA N 1 SRAGEN

3. Persamaan Ellips dengan pusat P (g, h)
Direktriks
y
x
0
A2
A1
F2
F1
P (g, h)
B2 B1
Direktriks
1
)()(
2
2
2
2




a
hy
b
gx
Matematika Peminatan
IRISAN KERUCUT (ELLIPS)
SMA N 1 SRAGEN
b
a

4. Perbandingan
Matematika Peminatan
IRISAN KERUCUT (ELLIPS)
SMA N 1 SRAGEN

5. Graph the following Ellipse
1
9
)3(
25
)2( 22



 yx
Center: (2, -3)
a = 5 in x direction
b = 3 in y direction
Contoh Soal :

6. Graph the following Ellipse
1
9
)3(
25
)2( 22



 yx
a = 5 b = 3 a2 = b2 + c2
52 = 32 + c2
25 = 9 + c2
16 = c2
4 = c

7. Graph the following Ellipse
1
9
)3(
25
)2( 22



 yx
a = 5 b = 3 c = 4 a
b
LR
2
2

5
18
LR
Find the Length of the LR.  
5
32
2
LR

8. Graph the following Ellipse
1
9
)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:
5
18

9. Exercise
1
324
)5(4
324
)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
1
81
)5(
36
)2( 22



 yx

10. Exercise
1
81
)5(
36
)2( 22



 yx
Center: (-2, 5)
a = 9 in y direction
b = 6 in x direction

11. Graph the following Ellipse
a = 9 b = 6 a2 = b2 + c2
92 = 62 + c2
81 = 36 + c2
45 = c2
c53
)535,2( 
)535,2( 
1
81
)5(
36
)2( 22



 yx
53
53

12. Graph the following Ellipse
1
81
)5(
36
)2( 22



 yx
a
b
LR
2
2

8LR
Find the
Length of
the LR.
a = 9 b = 6 c = 53
 
9
62
2
LR

13. Graph the following Ellipse
)535,2( 
)535,2( 
1
81
)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