\begin{definition}[Definition:Ovals of Cassini]
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 $b$.
\end{definition}