Negative pedal curve
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Negative pedal curve
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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'}](http://wpcontent.answcdn.com/wikipedia/en/math/a/5/8/a588ce2e39ab0f23e1d64d2fa9212179.png)
![Y[x,y]=\frac{(x'^2-y'^2)x'+2xyy'}{xy'-yx'}](http://wpcontent.answcdn.com/wikipedia/en/math/9/6/e/96ea79b8881ea384ebba265a2ed407db.png)
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