We learn to create the ellipse using the GSP.This, in my opinion, turns out to be the most useful and the most interesting drawing of the ellipse. With GSP we can create the ellipse and then move it and watch the changes occur in a dynamic way. Here’s a picture of the creation as well as a detailed explanation of how to make it on GSP.
1. Start by making a circle, C, with center F1.
2. Create a point on the outside of circle C and label it B. Also place a point, F2 anywhere inside of the circle.
3. Make a segment, l, from F2 to B and find the midpoint and call it M.
4. Construct a perpendicular bisector with l, or a perpendicular line with l through M, call this line q.
5. Now create a line through M and F1 and call it x.
6. Find the intersection of q and x and make a line through it and F2, call this intersection E.
7. Lastly, select E and B in that order, and go to Construct and Locus to create the ellipse.