Definition:Lemniscate of Bernoulli/Cartesian Definition

Definition
The lemniscate of Bernoulli is the curve defined by the Cartesian equation:
 * $\paren {x^2 + y^2}^2 = 2 a^2 \paren {x^2 - y^2}$


 * LemniscateOfBernoulli.png

Also defined as
Some sources give this as:
 * $\paren {x^2 + y^2}^2 = a^2 \paren {x^2 - y^2}$

which is the same but for a scale factor.

Also see

 * Equivalence of Definitions of Lemniscate of Bernoulli