Definition:Polar of Point/Circle

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Let $\CC$ be a circle whose radius is $r$ and whose center is at the origin of a Cartesian plane.

Let $P = \tuple {x_0, y_0}$ be an arbitrary point in the Cartesian plane.

The polar of $P$ with respect to $\CC$ is the straight line whose equation is given by:

$x x_0 + y y_0 = r^2$


Let $\LL$ be the polar of $P$ with respect to $\CC$.

Then $P$ is known as the pole of $\LL$.

Also see

  • Results about polars of points can be found here.