Focal points $ A,B $ are at distance $ 2 c $ apart. Find locus of a point $P$ so that sum of reciprocals of $AP,BP$ is a constant $ 2/a, a $ is the harmonic mean of these segments. Resemblance is to Cassinian ovals where their product is constant.
$$ \frac{1}{\sqrt{ (x-c)^2 + y^2}} + \frac{1}{\sqrt{ (x+c)^2 + y^2} }= \frac2a $$
