Circle of Apollonius in Complex Plane/Examples/mod z-3 over z+3 = 2/Proof 1

Proof
A point $P$ on this circle is $2$ times the distance from $z = 3$ as it is from $z = -3$.


 * Circle-of-Apollonius-(z-3)-(z+3).png

Let $z = x + i y$.

Hence the result by Equation of Circle in Complex Plane.