Hyperboloid of Two Sheet

Hyperboloid of Two Sheets is the surface of revolution of the curve family Hyperbola

hyperboloid2 DrC4B
hyperboloid2 
a = 1; b = 1; c = 1;
ParametricPlot3D[
 {{a*Sinh[u]*Cos[v], b*Sinh[u]*Sin[v], c*Cosh[u]},
  {a*Sinh[u]*Cos[v], b*Sinh[u]*Sin[v], -c*Cosh[u]}}
 , {u, 0, 3}, {v, -Pi, Pi}, BoundaryStyle -> {Thin, Gray},
 Axes -> False, Boxed -> False,
 PlotStyle ->
  Directive[RandomColor[], Opacity[0.7], Specularity[White, 30]]]

Conic Section Surfaces