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 N > 2 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.
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 the encloses all of them?