Equation of Circle/Cartesian/Corollary 2

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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: Cartesian, 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.

$\blacksquare$


Sources