Quadrilateral circumscribing a central conic

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If a quadrilateral circumscribes a central conic, the line joining the centers of its diagonals passes through the center of the conic.

Although the equation of the line is long, inspection shows it has only an X and a Y term, and no constant. Hence, it passes through the origin, which is the center of the ellipse.

Expressions

Name Input
Line IJ Eq Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image