The Ellipse on Sketchpad The instructions in this problem will construct an ellipse strict...

The Ellipse on Sketchpad The instructions in this problem will construct an ellipse strictly by geometry, using Sketchpad.

[1] Construct segment and locate points C and D on it (in the order A-C-D-B).

[2] Construct a circle centered at A passing dirough C. (Use Circle By Center and Point from the CONSTRUCT menu.)

[3] Construct segment using Segment from the CONSTRUCT menu. With still selected, select point D and choose Circle By Center and Radius.

[4] Select, or construct, the points of intersection E and F of the two circles. (If the circles do not intersect, move point D closer to point C.) Hide the circles.

[5] Select points E and F and choose Trace Points under DISPLAY.

As C is moved along segment , points E and F will trace out an ellipse with foci at .A and D. Explain why this is so, using the definition for an ellipse. Move D closer to A, then further away from A. What effect does this have on the ellipse?

NOTE: Save this construction for the next problem.