Definition:Polar of Point/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

  • Results about polars of points can be found here.


Sources