# Polar curve

Polar curve

For a plane curve given C by the equation $f\left(x_0,x_1,x_2\right)$and a point $a = \left(a_0,a_1,a_2\right)$, the polar curve$P_a\left(C\right)$ 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 $P_a\left(C\right)$ 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.

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

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