# Definition:Polar of Point/Circle

< Definition:Polar of Point(Redirected from Definition:Polar of Point wrt Circle)

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## 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