The pedal curve of a rectangular hyperbola with the pedal point at the focus is a circle (left figure; Hilbert and Cohn-Vossen 1999, p. 26). The pedal curve of a rectangular hyperbola with pedal point at the center is a lemniscate (right figure).
Hyperbola Pedal Curve
See also
Hyperbola, Pedal CurveExplore with Wolfram|Alpha
References
Ameseder, A. "Ueber Fusspunktcurven der Kegelschnitte." Archiv Math. u. Phys. 64, 143-144, 1879.Ameseder, A. "Zur Theorie der Fusspunktencurven der Kegelschnitte." Archiv Math. u. Phys. 64, 145-163, 1879.Hilbert, D. and Cohn-Vossen, S. Geometry and the Imagination. New York: Chelsea, 1999.Referenced on Wolfram|Alpha
Hyperbola Pedal CurveCite this as:
Weisstein, Eric W. "Hyperbola Pedal Curve." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HyperbolaPedalCurve.html