Parabola Pedal Curve

$\begin{figure}\begin{center}\BoxedEPSF{ParabolaPedalDirectorix.epsf scaled 400}\... ...\qquad\BoxedEPSF{ParabolaPedalFocusRefl.epsf scaled 400}\end{center}\end{figure}$

$\begin{figure}\begin{center}\BoxedEPSF{ParabolaPedalVertex.epsf scaled 450}\qquad\BoxedEPSF{ParabolaPedalFocus.epsf scaled 450}\end{center}\end{figure}$

On the Directrix, the Pedal Curve of a Parabola is a Strophoid (top left). On the foot of the Directrix, it is a Right Strophoid (top middle). On reflection of the Focus in the Directrix, it is a Maclaurin Trisectrix (top right). On the Vertex, it is a Cissoid of Diocles (bottom left). On the Focus, it is a straight line (bottom right).

References

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 94-97, 1972.