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Elliptic cylinder

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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=13326
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article