presentasi irisan kerucut ini membahas tentang persamaan ellips yang berpusat di P (M,N)

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