Equation of Circle

Theorem
The equation of a circle with radius $R$ and center $\tuple {a, b}$ can be expressed in the following forms:

Polar Coordinates
In polar coordinates, it does not make sense to refer to a point by $x$ and $y$ coordinates.

Instead, the center of a circle is commonly denoted $\polar {r_0, \varphi}$, where $r_0$ is the distance from the origin and $\varphi$ is the angle from the polar axis in the counterclockwise direction.

The equation for a circle with radius $R$ of this type is