Negative pedal curve

Circle — negative pedal curve of a limaçon

In the plane, for every point X other than P there is a unique line through X perpendicular to XP. For a given curve in the plane and a given fixed point P, called the pedal point, the negative pedal curve is the envelope of the lines XP for which X lies on the given curve.

The negative pedal curve of a pedal curve with the same pedal point is the original curve.

For a parametrically defined curve, its negative pedal curve with pedal point (0; 0) is defined as

$X[x,y]=\frac{(x'^2-y'^2)y'+2xyx'}{xy'-yx'}$

$Y[x,y]=\frac{(x'^2-y'^2)x'+2xyy'}{xy'-yx'}$

External links

• Negative pedal curve on Mathworld