Equation of Circle/Cartesian/Formulation 3

Equation of Circle in Cartesian Plane: Also presented as
Consider the equation of a circle with radius $R$ and center $\tuple {a, b}$ expressed in Cartesian coordinates:


 * $\paren {x - a}^2 + \paren {y - b}^2 = R^2$

This can also be presented as:
 * $x^2 + y^2 - 2 a x - 2 b y + a^2 + b^2 - R^2 = 0$

obtained by multiplying out and rearranging.