Elliptic Paraboloid


The trace in either the xz-plane or the yz-plane is a parabola.  The trace in a plane parallel to the xy-plane and "above" the xy-plane is an ellipse.

Ignore the labels on the axes.  The vertical axis is the z-axis.  Of the other two axes, the x-axis ranges from -10 to 10 and the y-axis ranges from -20 to 20.