Theorem 3.1: The equation of the circle whose center is   (x0, y0)   and whose radius is  r   is

(x - x0)2 + (y - y0)2 = r 2

Proof: By definition, the circle centered at   (x0, y0)   of radius   r   is the set of points whose distance from   (x0, y0)   is   r.   So if   (x, y)   is a point on the circle, the distance from   (x, y)   to   (x0, y0)   is

Square both sides and get

(x - x0)2 + (y - y0)2 = r 2

next theorem (3.2)