  If E is any ellipse inscribed in a convex quadrilateral, D, then we prove
that Area(E)/Area(D) is less than or equal to pi/4, and equality holds if and
only if D is a parallelogram and E is tangent to the sides of D at the
midpoints. This extends well known results for ellipses inscribed in triangles.
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.
