WORKSHEET 1

Place a large piece of graphing paper on a piece of cardboard.

1. Place the thumbtacks at (-8,0) and (8,0). Choose a string long enough to loop around both thumbtacks. Draw an ellipse.

2. Repeat Exercise 1 but place the thumbtacks at (-5,0) and (5,0). Use the same loop of string and draw an ellipse. How does this ellipse compare to the one in #1?

Place the thumbtacks at each set of points and draw an ellipse. You may change the length of

the loop of string if you like.

3. (12,0) and (-12,0) not included

4. (2,0) and (-2,0)

5. (10,4) and (-10,4)

For numbers 6-10, describe what happens to the shape of an ellipse when each change is made.

6. The thumbtacks are moved closer together.

7. The thumbtacks are moved farther apart.

8. The thumbtacks are arranged vertically.

9. One thumbtack is removed, and the string is looped around the remaining thumbtack.

10. Pick a point on one of the ellipses you have drawn. Use a ruler to measure the distances from that point to the points where the thumbtacks were located. Add the distances. Repeat for other points on the same ellipse. What relationship do you notice?