If a triangle is inscribed in a conic section, any line conjugate to one side meets the other two sides in conjugate points.
Seydewitz's Theorem
See also
Conic Section, TriangleExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Seydewitz's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SeydewitzsTheorem.html