The ebook Elementary Calculus is based on material originally written by H.J. Keisler. For more information please read the copyright pages.

Quadric Cylinders

If z does not appear in an equation, its graph will be a cylinder parallel to the z-axis. The cylinder is generated by a line parallel to the z-axis moving along a curve in the plane z = 0.

The graph (in space) of 11_partial_differentiation-4.gif is an elliptic cylinder.It intersects any horizontal plane z = z0 in an ellipse.

The graph of 11_partial_differentiation-5.gif is a parabolic cylinder.

The graph of 11_partial_differentiation-6.gif is a hyperbolic cylinder.

Cylinders parallel to other axes are similar. The three types of quadric cylinders are shown in Figure 11.1.4.


Figure 11.1.4

Last Update: 2006-11-17