Equation of Circle/Polar/Corollary

Corollary to Equation of Circle
Let $C$ be a circle whose radius is $R$.

Let $C$ be aligned in a polar coordinate frame such that its center is at the origin.

Then the equation of a $C$ is given by:
 * $r = R$

Proof
From Equation of Circle: Polar Form, we have a circle whose center is at $\left({r_0, \varphi}\right)$ whose radius is $R$ is:
 * $r^2 - 2 r r_0 \cos \left({\theta - \varphi}\right) + \left({r_0}\right)^2 = R^2$

So, when $\left({r_0, \varphi}\right) = \left({0, 0}\right)$: