Cylinders
Suppose we are given a plane in space that contains a curve, and in addition we are given a line that is not parallel to this plane. A cylinder is a surface that is generated by moving the curve through space, parallel to the given line. (Or, you can think of the cylinder as the collection of all lines passing through the curve that are parallel to the given line.) The curve is called a generating curve for the cylinder.
An equation in two variables defines a curve in a coordinate plane. For example, an equation in and defines a curve in the plane . A cylinder is then created by letting be unrestricted.