Locus of points $P$ on the plane such that $\overline{AP}=\lambda \cdot \overline{BP}$

Given two points on the plane $A$ and $B$ and given $\lambda \in (0,+\infty)$ consider the the locus of all the points $P$ such that $\overline{AP}=\lambda \cdot \overline{BP}$. If you study it with analytic geometry you will end up with the equation of a circle (degenerating to a stright line when $\lambda=1$).

• Question: is there a way to see that this locus is a circle only by geometrical arguments?