\begin{definition}[Definition:Lemniscate of Bernoulli/Focus]
Consider the '''lemniscate of Bernoulli'''  defined as the locus $M$ described by the equation:
:$P_1 M \times P_2 M = \paren {\dfrac {P_1 P_2} 2}^2$
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Each of the two points $P_1$ and $P_2$ can be referred to as a '''focus''' of the lemniscate.
\end{definition}