Equation of Unit Circle

Theorem
Let the unit circle have its center at the origin of the Cartesian $xy$ coordinate plane.

Its equation is given by:


 * $x^2 + y^2 = 1$

Proof
From Equation of Circle, the equation of a circle with radius $R$ and center $\left({a, b}\right)$ is:
 * $\left({x - a}\right)^2 + \left({y - b}\right)^2 = R^2$

Substituting $\left({0, 0}\right)$ for $\left({a, b}\right)$ and $1$ for $R$ gives the result.