Definition:Ovals of Cassini

Definition
Let $P_1$ and $P_2$ be points in the plane such that $P_1 P_2 = 2 a$ for some constant $a$.

The ovals of Cassini are the loci of points $M$ in the plane such that:
 * $P_1 M \times P_2 M = b^2$

for a real constant $b$.

Shape

 * Ovals-of-Cassini.png

Also see

 * Equation of Ovals of Cassini