College Algebra, 2013a

7.4 Ellipses 529
(x − 4) 2 (y − 2)2
8. + =1
8 18
Center (4, 2)
Major axis along x =4
Minor axis along y =2
Vertices (4, 2+3 √ 2), (4, 2 − 3 √ 2)
Endpoints of the Minor Axis
(4 − 2 √ 2, 2), (4 + 2 √ 2, 2)
Foci (4, 2+ √ 10), (4, 2 − √ 10)
e =
√
5
3
7
6
5
4
3
2
1
−1
−2
−3
y
1 2 3 4 5 6 7
x
(x − 3) 2 (y − 1)2
9. + =1
25 9
Center (3, 1)
Major Axis along y =1
Minor Axis along x =3
Vertices (8, 1), (−2, 1)
Endpoints of Minor Axis (3, 4), (3, −2)
Foci (7, 1), (−1, 1)
e = 4 5
x 2
(y − 5)2
10. + =1
3 12
Center (0, 5)
Major axis along x =0
Minor axis along y =5
Vertices (0, 5 − 2 √ 3), (0, 5+2 √ 3)
Endpoints of Minor Axis (− √ 3, 5), ( √ 3, 5)
Foci (0, 2), (0, 8)
e =
√
3
2
(x − 3) 2 (y +2)2
11. + =1
18 5
Center (3, −2)
Major axis along y = −2
Minor axis along x =3
Vertices (3 − 3 √ 2, −2), (3 + 3 √ 2, −2)
Endpoints of Minor Axis (3, −2 + √ 5),
(3, −2 − √ 5)
Foci (3 − √ 13, −2), (3 + √ 13, −2)
e =
√
26
6
(x − 1) 2 (y − 3)2
12. + =1
16 8
Center (1, 3)
Major Axis along y =3
Minor Axis along x =1
Vertices (5, 3), (−3, 3)
Endpoints of Minor Axis (1, 3+2 √ 2),
(1, 3 − 2 √ 2)
Foci (1 + 2 √ 2, 3), (1 − 2 √ 2, 3)
e =
√
2
2