the product of the distances to two fixed points PF_{1}·PF_{2} at distance 2a from each other is constant at a²: PF_{1}·PF_{2} = a² (wp)
It is a special case of the Cassini oval
locus of points in the plane such that:
the product of the distances to two fixed points is constant. (wp)
This may be contrasted to an ellipse, for which the sum of the distances is constant, rather than the product.
Cassini ovals are the special case of wp/Polynomial_lemniscate when the polynomial used has degree 2.
wp/Lemniscate_Building.gif | wp/Watt's_linkage