Difference between revisions of "Elliptic cylinder"
From Encyclopedia of Mathematics
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A cylindrical [[Surface of the second order|surface of the second order]] having an [[Ellipse|ellipse]] as directrix. If this ellipse is real, then the surface is called real and its canonical equation has the form | A cylindrical [[Surface of the second order|surface of the second order]] having an [[Ellipse|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 | 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} | ||
Latest revision as of 06:50, 23 January 2013
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
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