Copy of More about ellipses
Every ellipse can be constructed by rotating two points on concentric circles at the same rotational speed in opposite directions, and tracing the midpoint of the segment between them. The foci are included in this graphic,as are the related hyperbola and their asymptotes. In addition, the slopes of the asymptotes stem from the radii of the two circles. I'll leave the how a secret for a while.
The related hyperbola are also shown, but are not connected to the circles yet. (Directly, anyway.)