\begin{definition}[Definition:Circle of Apollonius]
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:
:$X A = \map \lambda {X B}$
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Then $X$ is a '''circle of Apollonius'''.
\end{definition}