Polar curve

For a plane curve given C by the equation $f(x\_0,x\_1,x\_2)$and a point $a\; =\; (a\_0,a\_1,a\_2)$, the polar curve$P\_a(C)$ is a curve given by the equation $a\_0\; f\_0\; +\; a\_1\; f\_1\; +\; a\_2\; f\_2\; =\; 0$, where $f\_i$ are partial derivatives.

The intersection of C and $P\_a(C)$ is the visible contourof C from the point a, i.e., the set of points p such that the tangentat p to C contains a. (picture needed).

Some common types of polar curves include the limacon, lemniscate, rose curve, cardioid, and spiral.

See also: Polar surface

"This article will be about the mathematics of polar curves. For its use in aviation see Polar curve (aviation)".