Definition: Let us define a semi-ellipse as either of the two halves into which an elliptical region is cut by any line that passes through its center. Obviously, all semi-ellipses that come from any given ellipse have same area and any given semi-ellipse determines a unique full ellipse.
Question: Given a convex n-gon, how could one find the least area semi-ellipse that can contain it? We need to find the full-ellipse and bisecting line that give the semi-ellipse.
Note 1: In the question, we can replace area with perimeter and so on.
Note 2: In the comments at Biconvex Lens - an 'oriented' convex container for planar point sets, we mentioned the algorithmic problems of finding the least area and least perimeter full ellipses that contain a specified convex n-gon.
