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Right: hyperboloid of two sheets (4).
Figure 3: Left: elliptic paraboloid (7). Right: hyperbolic paraboloid (8).
Surfaces with equations (9) --(17) are cylinders over the planes curves of the same equation (Section 13.2). Equations (2), (6), (10), (16), have no real solutions, so they do not describe surfaces in real three-dimensional space. A surface with equation (5) can be regarded as a cone (Section 13.3) over a conic C (any ellipse, parabola or hyperbola can be taken as the directrix; there is a two-parameter family of essentially distinct cones over it, determined by the position of the vertex with respect to C)...
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