Minimum-Area ellipse containing a finite set of points. II

We continue the investigation of the problem of construction of a minimum-area ellipse for a given convex polygon (this problem is solved for a rectangle and a trapezoid). For an arbitrary polygon, we prove that, in the case where the boundary of the minimum-area ellipse has exactly four or five common points with the polygon, this ellipse is the minimum-area ellipse for the quadrangles and pentagons formed by these common points. Translated from Ukrainskii Matematicheskii Zhurnal, Vol.50, No.8, pp. 1098–1105, August, 1998.