\begin{definition}[Definition:Lemniscate of Bernoulli/Parametric Definition]
The '''lemniscate of Bernoulli''' is the curve defined by the parametric equation:
:$\begin{cases} x = \dfrac {a \sqrt 2 \cos t} {\sin^2 t + 1} \\ y = \dfrac {a \sqrt 2 \cos t \sin t} {\sin^2 t + 1} \end{cases}$
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\end{definition}