cylindrical surface[sə′lin·drə·kəl ′sər·fəs]
(or cylinder), a surface traced by a line moving parallel to a given fixed line and intersecting a given curve. The fixed line is called the generatrix, and the curve is called the directrix.
If the generatrix of a cylindrical surface is parallel to the z-axis of a rectangular coordinate system, the equation of the surface is F(x, y) = 0. If the generatrix of a cylindrical surface is parallel to the line ax + by + c = 0 in the xy-plane, the equation of the surface has the form z = f(ax + by). If a circle, ellipse, hyperbola, or parabola is the directrix, the resulting cylindrical surface is said to be circular, elliptical, hyperbolic, or parabolic, respectively.