3D-model of quadric intersection with common focus points

The solution of the problem of quadric intersection combined with focus points or focus points of their sections is considered in the article. Ellipsoid, hyperboloid and paraboloid are quadrics formed by the rotation. All combinations of such quadrics are studied. It is shown that there is intersection by one or two conics. Peculiar features of spatial position of the quadric intersection lines are analyzed. It is shown that there are common periphery plane quadric such as elliptic cone or parabolic cylinder at adjustment of considered quadrics and necessary combination of parameters of a relative position. Moreover, common inner tangent sphere appears. The analysis is performed by 3d computer geometric simulation methods with AutoCAD. The examples and algorithms for tangent quadric construction are given. The connection between the problem in question and well-known Monge theorem is studied.