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 $\polar {r_0, \varphi}$ whose radius is $R$ is:
 * $r^2 - 2 r r_0 \, \map \cos {\theta - \varphi} + \paren {r_0}^2 = R^2$

So, when $\polar {r_0, \varphi} = \polar {0, 0}$: