Exercises on Ellipses Centered at the Origin
1. For the ellipse
x2
y2
+
= 1
9
4
the x-axis the ______________ axis and the y-axis is the ______________ axis.
2. For the ellipse
x2
y2
+
= 1
4
9
the x-axis the ______________ axis and the y-axis is the ______________ axis.
For exercises 3 and 4, answer true or false and explain your reasoning.
3. Ellipses are never graphs of functions.
4. The graph of 4x2 + 25y2 = 36 is not an ellipse since the right hand side is not equal to 1.
For exercises 5 - 12, sketch the graph of the given ellipse.
5.
x2
y2
+
= 1
25 9
6.
x2
y2
+
= 1
4 36
7.
x2
y2
+
= 1
36 49
8.
x2
y2
+
= 1
36 25
9.
y2
x2
+
= 1
4
10.
x2
+ y2 = 1
9
11.
x2
y2
+
= 1
5
16
12.
y2
x2
+
= 1
7
For exercises 9 - 32, sketch of the graph of the given ellipse.
13. y2
9x2
+
= 1
4
14.
x2
+ 16y2 = 1
4
15. 25x2 + y2 = 1
16. x2 + 16y2 = 1
17. 4x2 + 9y2 = 1
18. 100x2 + 81y2 = 1
19. 3x2 + 10y2 = 1
20. 18x2 + 11y2 = 1
21. x2 + 4y2 = 16
22. 9x2 + y2 = 36
23. x2 + 25y2 = 25
24. 25x2 + 4y2 = 100
25. x2 + 4y2 = 9
26. 16x2 + y2 = 25
27. 25 x2 + 36y2 = 9
28. 36x2 + 25y2 = 49
29. 9 x2 + 12y2 = 12
30. 4x2 + 64y2 = 8
31. x2 + 10y2 = 5
32. 6x2 + 15y2 = 9
For exercises 33 - 38 find the equation of the ellipse.
33. 
34. 
35. 
36. 
37. 
38. 
39. Two of the vertices of an ellipse centered at the origin are (3,0) and (0,-4). What are the other two vertices?
40. Two of the vertices of an ellipse centered at the origin are (-5,0) and (0,1). What are the other two vertices?
41. One of the vertices of an ellipse centered at the origin is (3,0).
If the ellipse passes through the point (1,8
/3),
find the equation of the ellipse.
42. One of the vertices of an ellipse centered at the origin is (0,-10).
If the ellipse passes through the point (
,5),
find the equation of the ellipse.
43. One of the vertices of an ellipse centered at the origin is (-3,0).
If the ellipse passes through the point (
,2),
find the equation of the ellipse.
44. Go to the site, Cool Math, and give two examples of how ellipses appear in the "real world".