# Pedal Equations?

Calculus Level 4

A relation between the distance $$r$$ of any point on a given curve from the origin and the length of the perpendicular $$p$$ from the origin to the tangent at that point is called Pedal Equation of the curve.

Consider a curve represented by the equation:
$c^{2}(x^{2} + y^{2}) = x^{2}y^{2}$
where $$c$$ is some constant.
If the Pedal Equation of this curve can be written in the form:
$\frac{\alpha}{p^{\beta}} + \frac{\gamma}{r^{\beta}} = \frac{\alpha}{c^{\beta}}$
where $$\alpha$$ , $$\beta$$ , $$\gamma$$ are positive coprime integers. Find the value of $$\alpha+\beta+\gamma$$

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