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If E is any ellipse inscribed in a convex quadrilateral, D -, then we prove that Area , and equality holds if and only if D is a parallelogram and E is tangent to the sides of D at the midpoints. We also prove that the foci of the unique ellipse of maximal area inscribed in a parallelogram, D -, lie on the orthogonal least squares line for the vertices of D -. This does not hold in general for convex quadrilaterals. the distance(Euclidean) from z j to l . In  the authors prove the followingdoi:10.7153/jmi-04-40 fatcat:fhizf6hfvjco3cgzenewlw5h34