# Definition:Polar of Point/Ellipse

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

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## Definition

Let $\EE$ be an ellipse embedded in a Cartesian plane in reduced form with the equation:

- $\dfrac {x^2} {a^2} + \dfrac {y^2} {b^2} = 1$

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

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

- $\dfrac {x x_0} {a^2} + \dfrac {y y_0} {b^2} = 1$

### Pole

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

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

## Also see

- Definition:Chord of Contact on Ellipse: when $P$ is specifically outside $\EE$

- Results about
**polars of points**can be found here.

## Sources

- 1933: D.M.Y. Sommerville:
*Analytical Conics*(3rd ed.) ... (previous) ... (next): Chapter $\text {IV}$. The Ellipse: $3$.