The "Cartesian ovals," sometimes also known as the Cartesian curve or oval of Descartes, are the quartic curve consisting of
two ovals. They were first studied by Descartes in 1637 and by Newton while classifying
cubic curves. It is the locus of a point whose distances from two foci and in two-center bipolar
coordinates satisfy

(1)

where
are positive integers, is a positive real, and and are the distances from and (Lockwood 1967, p. 188).

Cartesian ovals are anallagmatic curves. Unlike
the Cartesian ovals, these curves possess three foci.