  Let Q be a convex quadrilateral in the xy plane and let int(Q) denote the
interior of Q. Let D_1 and D_2 denote the diagonals of Q and let P denote their
point of intersection.
  For (i)-(iii), let P_0 = (x_0,y_0) be a point in the interior of Q. We prove
the following:
  (i) If P_0 does not lie on D_1 or on D_2, then there are exactly two ellipses
inscribed in Q which pass through P_0.
  (ii) If P_0 does lie on D_1 or on D_2, but does not equal P, then there is
exactly one ellipse inscribed in Q which passes through P_0.
  (iii) There is no ellipse inscribed in Q which passes through P.
  (iv) If P_0 lies on the boundary of Q, but P_0 is not one of the vertices of
Q, then there is exactly one ellipse inscribed in Q which passes through
P_0(and is thus tangent to Q at one of its sides).
