If $A$ and $B$ are points in the plane such that $\frac{P A}{P B}=k$ (constant) for all $P$ on a giv

Question

If $A$ and $B$ are points in the plane such that $\frac{P A}{P B}=k$ (constant) for all $P$ on a given circle, then the value of $k$ cannot be equal to ___?

Professor PC Thomas Classes · Answer

Given that the locus of $P$ is a circle and $\frac{P A}{P B}=k \quad$ (constant)\ If $k=1$, then $P A=P B$\ $\Rightarrow P$ lies on the $\perp r$ bisector or $A B$\ $	herefore \quad k 
eq 1$, which is a contradiction.\