Definition:Polar of Point/Circle

Definition

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:

$x x_0 + y y_0 = r^2$

Pole

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

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

Also see

• Definition:Chord of Contact on Circle: when $P$ is specifically outside $\CC$

• Results about polars of points can be found here.

Sources

• 1933: D.M.Y. Sommerville: Analytical Conics (3rd ed.) ... (previous) ... (next): Chapter $\text {III}$. The Circle: $4$. Pole and polar