# 4.6: The Cylinder

In three-dimensional solid geometry the equation

\[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \label{4.6.1}\]

represents a cylinder of elliptical cross-section, whose axis coincides with the \(z\)-axis. The equation to a cylinder with an axis in another position and with another orientation can be obtained by the usual processes of translation and rotation of axes (see Section 3.7).