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In this note, the ideas employed in  to treat the problem of an ellipsoid intersected by a plane are applied to the analogous problem of a hyperboloid being intersected by a plane. The curves of intersection resulting in this case are not only ellipses but rather all types of conics: ellipses, hyperbolas and parabolas. In text books of mathematics usually only cases are treated, where the planes of intersection are parallel to the coordinate planes. Here the general case is illustrated with intersecting planes which are not necessarily parallel to the coordinate planes.
Until recently, the effects of all injectable filling agents were temporary and very rarely associated with permanent problems. In the past, the permanent injectable silicone had been used but had been so problematic that the Justice Department filed injunctions against certain physicians on behalf of the FDA. After 2000 a dangerous pattern grew in the corridors of Washington DC, where politics and money changed the face of America and the field of aesthetics to the detriment of the faces of the consumers. Industry has accomplished the approval of synthetic agents that should have never reached the market. Once injected under skin, the body cannot digest these agents and the immune system walls them off with resultant formation of nodules, which at times require surgical removal.