TOPICS
Search

Frégier's Theorem


FregiersTheorem

Frégier's theorem states that if a right angle with vertex P on a nondegenerate conic section meets the conic section again at A and B, then the line AB passes through a fixed point P^' in the projective plane, independent of the right angle, as illustrated above.

For a rectangular hyperbola, the hypotenuse lines AB are parallel, so their common point P^' is a point at infinity (Prisacariu 2022).


See also

Conic Section, Right Angle

Explore with Wolfram|Alpha

References

Prisacariu, R. "Frégier's Theorem and Frégier Points." Apr. 7, 2022. https://www.raulprisacariu.com/math/fregiers-theorem-and-fregier-points/.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. Middlesex, England: Penguin Books, p. 83, 1991.

Referenced on Wolfram|Alpha

Frégier's Theorem

Cite this as:

Weisstein, Eric W. "Frégier's Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FregiersTheorem.html

Subject classifications