Editing Pedal curve (section)

===From the pedal equation===
The [[pedal equation]]s of a curve and its pedal are closely related. If ''P'' is taken as the pedal point and the origin then it can be shown that the angle ψ between the curve and the radius vector at a point ''R'' is equal to the corresponding angle for the pedal curve at the point ''X''. If ''p'' is the length of the perpendicular drawn from ''P'' to the tangent of the curve (i.e. ''PX'') and ''q'' is the length of the corresponding perpendicular drawn from ''P'' to the tangent to the pedal, then by similar triangles
:<math>\frac{p}{r}=\frac{q}{p}.</math>
It follows immediately that the if the pedal equation of the curve is ''f''(''p'',''r'')=0 then the pedal equation for the pedal curve is<ref>Williamson p. 228</ref>
:<math>f(r,\frac{r^2}{p})=0</math>

From this all the positive and negative pedals can be computed easily if the pedal equation of the curve is known.