**Theorem 3.1**: The equation
of the circle whose center is (*x*_{0}, *y*_{0}) and whose radius is *r* is

**Proof**: By definition, the
circle centered at (*x*_{0}, *y*_{0}) of radius *r *is the set of points whose distance from (*x*_{0}, *y*_{0}) is *r*. So if (*x*, *y*) is a point on the
circle, the
distance from (*x*, *y*) to (*x*_{0}, *y*_{0}) is

Square both sides and get