Definition:Circle of Apollonius

Definition
Let $A, B$ be distinct points in the plane.

Let $\lambda \in \R_{>0}$ be a strictly positive real number.

Let $X$ be the locus of points in the plane such that:
 * $XA = \lambda \paren {XB}$


 * Circle-of-Apollonius.png

Then $X$ is a circle of Apollonius.

Also see

 * Circle of Apollonius is Circle