Definition:Polar of Point/Ellipse

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:


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

Also see

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