Minthorn's conjecture on centers of conics through a quadrilateral's vertices

Let $Q$ be a quadrilateral, and consider all conics passing through its four vertices. Minthorn's conjecture. If $Q$ is convex, the set of centers of these conics is a hyperbola; if $Q$ is not convex, the set is an ellipse. This conjecture was proved by Maud Minthorn in 1912, and the paper supplies a shorter elementary proof.