Classification of the relative positions between a hyperboloid and a   sphere
  We characterize all possible relative positions between a hyperboloid of one sheet and a sphere through the roots of a characteristic polynomial associated to these quadrics. The classification is also suitable for a hyperboloid and a ellipsoid in some situations.   As an application, this provides a method to detect contact between the two surfaces by a simple calculation in many real world applications. 
M. Brozos-V\'azquez, M.J. Pereira-S\'aez, M.J. Souto-Salorio, Ana D.   Tarr\'io-Tobar
math.MG