Given a set of N > 2 (two-dimensional and coplanar) ellipses, all centered at the origin, how do I find the ellipse with the minimum area which encloses all of them?

**Background:**

Thanks to Will Jagy for answering my similar question re: two ellipses. I had initially naively thought I could apply this solution to a set of more than two ellipses, all centered at the origin, simply by iterating through the set, using the previously calculated enclosing ellipse and the next ellipse in the set to arrive at the solution I wanted. However, as Will pointed out to me, this algorithm is not guaranteed to give the minimum-area enclosing ellipse for every set of ellipses. And thus, my new question.