In this case we take the ellipse as a point locus, and construct the normal from point K to the tangent at each point of the curve. The envelope of these constructed intersection points then generates the required pedal curve.



Click the linked diagram below, and then click the ‘Animate’ button to generate the pedal curve of the ellipse relative to point K. Clicking the little red x which appears at bottom right will clear the drawing from the applet window. Now drag the red point Q slowly around the circle. Notice that we have some choice in the position of the point K. You may be especially interested in looking at the cases when K lies on the ellipse (two positions) and when K lies at a focus (O ). What are the pedal curves here?

For this curve we obtain some familiar-looking curves as pedal curves. When K lies at a focus the pedal curve is a circle. When K lies on or outside the ellipse, the pedal curve looks like a cardioid or limaçon, but it appears that in fact it is not.

Bibliography

http://mathworld.wolfram.com/EllipsePedalCurve.html