Definition:Polar of Point

Definition

Circle

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:

$x x_0 + y y_0 = r^2$

Ellipse

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:

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