Pedal equation

For a plane curve C and a given fixed point O, the pedal equation of the curve is a relation between r and p where r is the distance from O to a point on C and p is the perpendicular distance from O to the tangent line to C at the point. The point O is called the pedal point and the values r and p are sometimes called the pedal coordinates of a point relative to the curve and the pedal point. It is also useful to measure the distance of O to the normal ${\displaystyle p_{c}}$ (the contrapedal coordinate) even though it is not an independent quantity and it relates to ${\displaystyle (r,p)}$ as ${\displaystyle p_{c}:={\sqrt {r^{2}-p^{2}}}}$.

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