# Descartes oval

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A plane curve for which the distances and between any point of the curve and two fixed points and (the foci) are related by the non-homogeneous linear equation A Descartes oval may be defined by means of the homogeneous linear equation where is the distance to the third focus located on the straight line . In the general case, a Descartes oval consists of two closed curves, one enclosing the other (see Fig.). The equation of a Descartes oval in Cartesian coordinates is where is the length of the segment . If and , the Descartes oval is an ellipse; if and , it is a hyperbola; if , it is a Pascal limaçon. First studied by R. Descartes in the context of problems of optics . Figure: d031340a

How to Cite This Entry:
Descartes oval. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Descartes_oval&oldid=16712
This article was adapted from an original article by E.V. Shikin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article