\begin{definition}[Definition:Ovals of Cassini/Shape]
Let $P_1$ and $P_2$ be points in the plane such that $P_1 P_2 = 2 a$ for some constant $a$.
Let the '''ovals of Cassini''' be defined as the loci of points $M$ in the plane such that:
:$P_1 M \times P_2 M = b^2$
for real constant $b$.
When $b > a$, $M$ is in one continuous piece, either oval or bone-shaped.
When $b < a$, $M$ is in two separate pieces, each surrounding one of the foci of $M$.
When $b = a$, $M$ degenerates into the lemniscate of Bernoulli.
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\end{definition}