Take two poles O1 and O2. Then you can define the Cartesian oval as the collection of points for which the distance to O1 and the distance to O2 are linearly related.

Cartesian ovals were first studied by René Descartes in 1637. For this reason they are frequently called the 'Ovals of Descartes'.

These curves were also studied by Newton in his classification of cubic curves.

Cartesian Ovals are anallagmatic curves.

The Cartesian oval has a bipolar equation:

*r + mr' =a. *