The lemniscate of Bernoulli may be defined as the locus of a point which moves so that the product of its distances from two fixed points is constant and is equal to the square of half the distance between these points.
2
The name lemniscate is sometimes given to any crunodal quartic curve having only one real finite branch which is symmetric about the axis.
3
The same name is also given to the first positive pedal of any central conic. When the conic is a rectangular hyperbola, the curve is the lemniscate of Bernoulli previously described.