Manipulate[Plot3D[x^2+c,{x, -5, 5}, {y, -5, 5},PlotRange->15,BoxRatios->Automatic, ColorFunction->"CoffeeTones"], {c, {-10, -5, 0, 5, 10}}]

Manipulate[Plot3D[{Sqrt[-x^2+-y^2 +c], -Sqrt[-x^2+-y^2+c]},{x, -15, 15}, {y, -15, 15}, PlotRange->15,BoxRatios->Automatic, ColorFunction->"CoffeeTones"], {c, {50, 100, 150, 200}}]

Manipulate[Plot3D[{Sqrt[x^2+y^2 -c], -Sqrt[x^2+y^2-c]},{x, -10, 10}, {y, -10, 10}, BoxRatios->Automatic, ColorFunction->"CoffeeTones"], {c, {-10, -5, 0, 5, 10}}]