Equation of Circle center Origin

Theorem
The equation of a circle with radius $R$ whose center is at the origin expressed in Cartesian coordinates is:


 * $x^2 + y^2 = R^2$

Proof
From Equation of Circle in Cartesian Plane, the equation of a circle with radius $R$ and center $\tuple {a, b}$ expressed in Cartesian coordinates is:


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

Setting $a = b = 0$ yields the result.