Lamp Hyperbola

(* 2d *)
r = 1; Manipulate[
 Show[ParametricPlot[{-Y Cos[\[Theta]]/Sin[\[Theta]],
    Y h/(r Sin[\[Theta]])}, {\[Theta], 0.1, Pi - 0.1},
   PlotRange -> {{-4, 4}, {0, 10}}],
  ParametricPlot[Y {Sinh[t], h /r Cosh[t]}, {t, -3, 3}]]
 , {Y, 1, 3}, {h, 0.1, 3}]

(* 3d *)
r = 1; Manipulate[

 Show[ParametricPlot3D[{Sin[\[Theta]], Cos[\[Theta]], z}, {\[Theta],
    0, 2 Pi}, {z, h, -h}, PlotStyle -> Red,
   Lighting -> {{"Point", White, {0, 0, 0}}},
   PlotRange -> {{-4, 4}, {-3, 2}, {-3, 10}}, ViewPoint -> {-1, 2, 1},
    Boxed -> False, Axes -> None],
  Graphics3D[{White,
    Polygon[{{-4, -Y, -3}, {4, -Y, -3}, {4, -Y, 10}, {-4, -Y, 10}}]}],
  ParametricPlot3D[{Y Sinh[t], -Y + 0.01, Y h /r Cosh[t] + z}, {t, -3,
     3}, {z, 0, 10}, MeshStyle -> None]
  ]
 , {{Y, 2}, 1, 3}, {{h, 1}, 0.1, 3}]