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.