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Pole and polar

In geometry, the pole and polar are respectively a point and a line that have a unique reciprocal relationship with respect to a given conic section. If the point lies on the conic section, its polar is the tangent line to the conic section at that point.
For a given circle, reciprocation in a circle means the transformation of each point in the plane into its polar line and each line in the plane into its pole.
==Properties==

Poles and polars have several useful properties:
* If a point P lies on a line ''l'', then the pole L of the line ''l'' lies on the polar ''p'' of point P.
* If a point P moves along a line ''l'', its polar ''p'' rotates about the pole L of the line ''l''.
* If two tangent lines can be drawn from a pole to the conic section, then its polar passes through both tangent points.
* If a point lies on the conic section, its polar is the tangent through this point to the conic section.
* If a point P lies on its own polar line, then P is on the conic section.
* Each line has, with respect to a non-degenerated conic section, exactly one pole.

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