Visualising a saddle surface using contours and cross sections
This applet visualises the surface . Shown in light blue is the horizontal plane at z = c, and the contour of the surface at z = c (in dark blue if c > 0 or red if c < 0). The contour is the intersection of the plane at z = c with the surface Use the slider to adjust c. As c changes, the contours trace out the surface . Also shown is the cross section of the surface in the yz-plane, which has equation , x = 0 (in darker blue) and the cross section of the surface in the xz-plane, which has equation , y = 0.
The surface is an example of a hyperbolic paraboloid.