Pole and polar

（重定向自Polar reciprocation）

The polar line q to a point Q with respect to a circle of radius r centered on the point O. The point P is the inversion point of Q; the polar is the line through P that is perpendicular to the line containing O, P and Q.

If a point A lies on the polar line q of another point Q, then Q lies on the polar line a of A. More generally, the polars of all the points on the line q must pass through its pole Q.

Illustration of the duality between points and lines, and the double meaning of

Line p is the polar line to point P, l to L and m to M

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.

单词	Polar reciprocation
释义	Polar reciprocation 英语百科 Pole and polar （重定向自Polar reciprocation） 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.
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