Definition:Polar of Point/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