Definition:Lemniscate of Bernoulli/Cartesian Definition/Also defined as

Definition
Some sources define the Cartesian equation for the lemniscate of Bernoulli as:
 * $\paren {x^2 + y^2}^2 = a^2 \paren {x^2 - y^2}$

which is the same but for a scale factor:


 * LemniscateOfBernoulli-alsodefinedas.png

Its associated parametric equation is:
 * $\begin {cases} x = \dfrac {a \cos t} {\sin^2 t + 1} \\ y = \dfrac {a \cos t \sin t} {\sin^2 t + 1} \end{cases}$

Also see

 * Equivalence of Definitions of Lemniscate of Bernoulli