Cutting a plot off at a particular point on one axis, and also plotting a plane through that point to see a trace clearly.

ContourPlot3D[ {x^2 + y^2 - z^2 == 1, y==0}, {x,-2,2},{y,-2,0},{z,-2,2}]

Using the “Plot3D” command to plot an explicit surface.

Plot3D[ x^2 - y^2, {x,-3,3}, {y,-3,3} ]

Exploring the effect of the a, b, and/or c coefficients on the shape of a hyperboloid.

ContourPlot3D[ x^2 + y^2 - z^2 == 1, {x,-2,2}, {y,-2,2},{z,-2,2}]

ContourPlot3D[ x^2 /4+ y^2/4 - z^2 == 1, {x,-4,4}, {y,-4,4},{z,-2,2}]