Beitr\"age zur Algebra und Geometrie Contributions to Algebra and Geometry Volume 36 (1995), No. 1 Polarity of Embedded and Circumscribed Ellipsoids Friedrich Juhnke In this paper we investigate simultaneously the minimal circumscribed and the maximal inscribed ellipsoid of an $n-$dimensional convex body by means of optimization techniques. This approach presents necessary and sufficient optimality conditions and allows to establish polarity relations between these two extremal ellipsoids.