Hyperboloid of Two Sheets is the surface of revolution of the curve family Hyperbola.
a = 1; b = 1; c = 2; ParametricPlot3D[{a*Sinh[u]*Cos[v], b*Sinh[u]*Sin[v], c*Cosh[u]}, {u, 0, 3}, {v, 0, 6}].
Other algebaric surfaces that has cross-sections of conic sections are: ellipsoid, paraboloid, hyperbolic paraboloid, hyperboloid of one sheet, hyperboloid of two sheets.
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