Polar curve

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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 contour of C from the point a, i.e., the set of points p such that the tangent at 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).