An area inequality for ellipses inscribed in quadrilaterals

Alan Horwitz
2010 Journal of Mathematical Inequalities  
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 [5] the authors prove the following
more » ... rove the following results. Mathematics subject classification (2010): 52A38.
doi:10.7153/jmi-04-40 fatcat:fhizf6hfvjco3cgzenewlw5h34