Elliptic cylinder
From HandWiki
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}
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