1. Write an equations in both standard and general forms for each ellipse.
a.
b.
c.
2. Graph each ellipse. Identify the vertices, and co-vertices. Find the lengths of the major and minor axes.
x 2 y2

1
a.
9 16
b.
4x2 + 9y2 = 36
c. 4(x − 3)2 + 9(y + 2)2 = 36
3. Use completing the square to change each general form ellipse to standard form.
a. 9x2 + 4y2 + 8y − 32 = 0
b. x2 + 4y2 + 6x − 8y − 3 = 0
Identify the center, vertices, co-vertices, foci, length of the major and minor axis of each.
4.
𝑥2
49
+
5.
𝑥2
36
+ 16 = 1
6.
𝑥2
25
+ 49 = 1
7.
𝑦2
169
𝑦2
𝑦2
(𝑥+9)2
81
8.
=1
+
(𝑥−5)2
1
𝑦−1)2
4
+
=1
(𝑦+4)2
64
=1
9.
(𝑥−4)2
4
+
(𝑦−8)2
36
=1
10.
(𝑥−9)2
9
+
(𝑦−2)2
1
=1
11.
(𝑥−7)2
49
+
(𝑦+2)2
36
=1
Identify the center, vertices, co-vertices, foci, length of the major and minor axis of each. Then graph each equation
12.
𝑥2
4
+
𝑦2
9
=1
13.
𝑥2
49
14.
𝑥2
9
+
𝑦2
49
=1
15.
(𝑥−1)2
4
+ 𝑦2 = 1
+
𝑦2
49
=1
Write each equation in standard form. Identify the center, vertices, co-vertices, foci, length of the major and minor axis
of each.
16. 8x2 + 2y2 = 32
17. x2 + 4y2 + 2x - 24y + 33 = 0
18. 4x2 + 9y2 + 24x - 90y = -225
19. 25x2 + 4y2 - 200x - 8y + 304 = 0
20. 9x2 + 16y2 - 54x + 64y + 1 = 0
21. x2 + 121y2 - 726y + 968 = 0
22. 16x2 + 4y2 + 96x - 8y + 84 = 0
23. 4x2 + 9y2 + 96x - 16y - 11 = 0
Change the following to general form
24.
𝑥2
9
+
(𝑦−1)2
25
=1
25.
(𝑥−3)2
64
+
(𝑦+1)2
36
=1
Use the following information provided to write the standard form equation of each ellipse.
26. vertices (10, 0) and (-10, 0); co-vertices (0, 9) and (0, -9)
27. vertices (0, 6) and (0, -6); co-vertices (5, 0) and (-5, 0)
28. center (7, -10); vertex (-6, -10), co-vertex (7, -17)
29. center (1, -7); vertex (1, 1), c2 = 55
30. center (4, -8); height 18, width 14
31. major axis is vertical, center (8, -2); major axis is 18 units long; minor axis is 8 units long
32. Center at (2, 5) with the longer axis of length 12 and parallel to the x-axis, shorter axis of length 10.
33. Center at (-3, 4) with the longer axis of length 8 and parallel to the y-axis, shorter axis of length 2.
34. center (0, 0) with vertex (0, 2) and co-vertex (-1, 0)
35. center (-2, 3) having major axis length 10 and minor axis length 6
36. vertices (-2, 2) and (4, 2) and co-vertices at (1, 4) and (1, 0)
37. vertex at (-5, 1) and co-vertex at (-3, 2)