Concyclic Points of Two Ellipses with Orthogonal Axes

Given two ellipses with orthogonal axes.

If there are four points of intersection, all four are concyclic.

Click here for proofs by Alexander Bogomolny.

Remark. A more general statement is true: given two conics with orthogonal axes. If there are four points of intersection, all four are concyclic.


Oai Thanh Đào pointed out that the statement holds also if the axes are parallel.