# Elliptic cylinder

From Encyclopedia of Mathematics

A cylindrical surface of the second order having an ellipse as directrix. If this ellipse is real, then the surface is called real and its canonical equation has the form
\begin{equation}
\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1;
\end{equation}

if the ellipse is imaginary, then the surface is called imaginary and its canonical equation has the form \begin{equation} \frac{x^2}{a^2} + \frac{y^2}{b^2} = -1. \end{equation}

**How to Cite This Entry:**

Elliptic cylinder.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Elliptic_cylinder&oldid=29337

This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article