Frégier's theorem states that if a right angle with vertex
on a nondegenerate conic section meets the conic
section again at
and
,
then the line
passes through a fixed point
in the projective
plane, independent of the right angle, as illustrated
above.
For a rectangular hyperbola, the hypotenuse lines are parallel, so their common
point
is a point at infinity
(Prisacariu 2022).