Intersections of Rotational Quadratic Hypersurfaces with a Common Focus

Abstract This paper deals with rotational quadratic hypersurfaces in an n -dimensional Euclidean space. Namely, we explore some basic properties of the intersection of two rotational quadratic hypersurfaces that have a common focus, but are not necessarily confocal. We prove that any such intersection lies in at most two hyperplanes, and we specify the maximum number of its connected components.