\begin{definition}[Definition:Lemniscate of Bernoulli/Polar Definition/Also defined as]
Some sources define the polar equation for the '''lemniscate of Bernoulli''' as:
:$r^2 = a^2 \cos 2 \theta$
which is the same but for a scale factor:
:620px
Its associated parametric equation is:
:$\begin {cases} x = \dfrac {a \cos t} {\sin^2 t + 1} \\ y = \dfrac {a \cos t \sin t} {\sin^2 t + 1} \end{cases}$
\end{definition}