Definition:Lemniscate of Bernoulli/Geometric Definition

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 lemniscate of Bernoulli is the locus of points $M$ in the plane such that:
 * $P_1 M \times P_2 M = a^2$


 * LemniscateOfBernoulli.png

Also see

 * Equivalence of Definitions of Lemniscate of Bernoulli
 * Lemniscate of Bernoulli is Special Case of Ovals of Cassini