1. ellipse

2. Ellipse
The set of all co-planar points whose sum of the distances from two fixed points (foci) are constant.

3. Definition of major and minor axis
Ellipse
Definition of major and minor axis
minor axis
major axis

4. Ellipse
major axis
minor axis

5. Definition of vertices
Ellipse
Definition of vertices
and co-vertices
co-verticies
verticies
verticies
endpoint of major axis
co-verticies
endpoint of minor axis

6. Ellipse a2 = b2 + c2 Distance from center to vertex = a
Distance from center to co-vertex = b
Distance from center to foci = c b c a
Length of major axis = 2a
Length of minor axis = 2b
a2 = b2 + c2

7. Ellipse - horizontal a2 = b2 + c2 b c a
Distance from center to vertex = a
a2 = b2 + c2
Distance from center to co-vertex = b
Distance from center to foci = c

8. Ellipse - vertical a2 = b2 + c2 a c b
Distance from center to vertex = a
Distance from center to co-vertex = b
Distance from center to foci = c

9. Graph the following Ellipse
Center: (2, -3)
a = 5 in x direction
b = 3 in y direction
(2, 0) 3
(2, -3)
(-3, -3)
(7, -3) 5 5 3
(2, -6)

10. Graph the following Ellipse
a = 5 b = 3
a2 = b2 + c2
52 = 32 + c2
25 = 9 + c2
foci
16 = c2
4 = c
(2, 0) 3
(-2, -3)
(2, -3)
(6, -3)
(-3, -3)
(7, -3) 5 5 3
(2, -6)

11. Graph the following Ellipse
(-1, 12)
Center: (-1, 5) 7
a = 7 in y direction
(-1, 5)
(-5, 5)
(3, 5) 4 4
b = 4 in x direction 7
(-1, -2)

12. Graph the following Ellipse
a = 7 b = 4
a2 = b2 + c2
72 = 42 + c2
49 = 16 + c2
(-1, 12)
33 = c2
foci 7
5.7 = c
(-1, 5)
(-5, 5)
(3, 5) 4 4 7
(-1, -2)

13. Graph the following Ellipse
Center: (-1, -3)
a = 3 in x direction
b = 2 in y direction
(-1, -1) 2
(-1, -3)
(-4, -3)
(2, -3) 3 3 2
(-1, -5)

14. Graph the following Ellipse
a = 3 b = 2
a2 = b2 + c2
32 = 22 + c2
9 = 4 + c2
foci
5 = c2
(-1, -1)
2.2 = c 2
(-1, -3)
(-4, -3)
(2, -3) 3 3 2
(-1, -5)

15. Graph the following Ellipse
Center: (-2, 5)
a = 9 in y direction
b = 6 in x direction
(-2, 14) 9
(-2, 5)
(-8, 5)
(4, 5) 6 6 9
(-2, -4)

16. Graph the following Ellipse
a = 9 b = 6
a2 = b2 + c2
92 = 62 + c2
81 = 36 + c2
(-2, 14)
45 = c2
foci 9
6.7 = c
(-2, 5)
(-8, 5)
(4, 5) 6 6 9
(-2, -4)

17. Graph the following Ellipse
Center: (4, 3)
a = 5 in x direction
b = 2 in y direction
(4, 5) 2
(4, 3)
(-1, 3)
(9, 3) 5 5 2
(4, 1)

18. Graph the following Ellipse
a = 5 b = 2
a2 = b2 + c2
52 = 22 + c2
25 = 4 + c2
foci
21 = c2
(4, 5)
4.6 = c 2
(4, 3)
(-1, 3)
(9, 3) 5 5 2
(4, 1)