Cassini oval

The Cassini oval has the remarkable property that the product of distances to two foci are constant.

It is a special case of the Cassini oval and is a rational algebraic curve of degree 4.

A Cassini oval, by contrast, is the locus of points for which the product of these distances is constant.

In addition, foci are used to define the Cassini oval and the Cartesian oval.

Examples include the hippopede and the Cassini oval and their relatives, such as the lemniscate of Bernoulli.

The term "bipolar" is often used to describe other curves having two singular points (foci), such as ellipses, hyperbolas, and Cassini ovals.

The most famous spiric section is the Cassini oval, which is the locus of points having a constant product of distances to two foci.

Cassini ovals are named after the astronomer Giovanni Domenico Cassini who studied them in 1680.

Cassini ovals (including the lemniscate of Bernoulli), toric sections and limaçons (including the cardioid) are bicircular quartics.

A Cassini oval is a set of points such that the product of the distances from any of its points to two fixed points is a constant.

Spiric sections are included in the family of toric sections and include the family of hippopedes and the family of Cassini ovals.

Examples of the most studied classes of algebraic varieties are: plane algebraic curves, which include lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves and quartic curves like lemniscates, and Cassini ovals.

When p is a polynomial of degree 1 then the resulting curve is simply a circle whose center is the zero of p. When p is a polynomial of degree 2 then the curve is a Cassini oval.