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Related to Hyperboloids: Hyperboloid of one sheet, Hyperboloid of two sheets, hyperbolic cylinder, Ellipsoids
open centric surfaces of the second degree. Two types of hyperboloids are distinguished: hyperboloid of one sheet (Figure 1) and hyperboloid of two sheets (Figure 2). They represent two of the five principal types of
second-degree surfaces and, on intersection with various planes, give all the conic sections—the ellipse, hyperbola, and parabola—as well as pairs of straight lines (in the case of a hyperboloid of one sheet). A hyperboloid comes infinitely close to a conic surface (the so-called asymptotic cone). The hyperboloid of one sheet is a ruled surface. In the corresponding coordinate system (see Figures 1 and 2), the equations of the hyperboloids have the form