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 $\left({a, b}\right)$ expressed in Cartesian coordinates is:

$\left({x - a}\right)^2 + \left({y - b}\right)^2 = R^2$

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

$\blacksquare$


Sources