Ellipse Pedal Curve
The pedal curve of an ellipse with parametric equations
x = acost
(1)
y = bsint
(2)
and pedal point (x_0,y_0) is given by
![画像:(a[ax_0sin^2t+bcost(b-y_0sint)])/(b^2cos^2t+a^2sin^2t)](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/EllipsePedalCurve/Inline10.svg){kind=link}
![画像:(b[by_0cos^2t+asint(a-x_0cost)])/(b^2cos^2t+a^2sin^2t).](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/EllipsePedalCurve/Inline13.svg){kind=link}
EllipsePedalFocus
The pedal curve of an ellipse with pedal point at the focus is a circle (Hilbert and Cohn-Vossen 1999, pp. 25-26).
EllipsePedal
For other pedal points, the pedal curves are more complicated, as illustrated above.
See also
Ellipse, Ellipse Negative Pedal Curve, Pedal CurveExplore with Wolfram|Alpha
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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
Ellipse Pedal CurveCite this as:
Weisstein, Eric W. "Ellipse Pedal Curve." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EllipsePedalCurve.html