Ellipse and Hyperbola Graphing

Instructions

1. Click and drag on the different colored "handles" to change the denominators of the two terms on the left and the constant on the right
2. If the graph goes away, it is probably because something impossible was requested (like dividing by zero!)

Questions

1. What are the four vertices of the ellipse x²/36+y²/100=1?

2. What are the two foci of the ellipse x²/36+y²/100=1?

3. What values of a, b, and c make an ellipse that has a horizontal major axis of 6 and a minor axis of 4?

4. What values of a, b, and c would make another ellipse with a vertical major axis of 6 and a minor axis of 4?

5. What values of a, b, and c make an ellipse that has a vertical major axis of 10 and a minor axis of 6?

6. a and b only go up to 100, what settings could you select to have it draw an ellipse that has a major axis of 32, and a minor axis of 24? (Specify a= , b= c=)

7. What is the correct standard form of the equation of the last question?

8. What is the equation of the ellipse that goes through (5,0) and (0,4)?

9. Where are the foci of the ellipse of the last question?

10. Set a=16, b=4 and c=1. What kind of shape is this?

11. What values of a, b, and c would make a hyperbola go up and down where it crosses the y axis at (0,3) and (0,-3) as well as the point (10,6)?

12. In this applet, you can only put in integer values. Is the answer to the last question exact? If not, what would be the exact equation that would go through (0,3), (0,-3) and (10,6)?

13. Where are the foci of the hyperbola that goes through (4,0), (-4,0) and (5,4)?