I'm looking for an analytic proof the statement for a Circle of Apollonius (I found a geometrical one already): If $\overline{AC}:\overline{BC}=s$, then $P \in k_s$. $s \in (0,1)$.
$k_s$ is the circle. I made the following drawing:
WLOG I can set $A=(0/0)$ and $B=(0/1)$. I really don't know how to go on. Perhaps someone can give a hint?
Greetings