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Friday 5 October 2012

Parametric equations of Hyperbola

East-west opening hyperbola:
\begin{matrix} x = a\sec t + h \\ y = b\tan t + k \\ \end{matrix} \qquad \mathrm{or} \qquad\begin{matrix} x = \pm a\cosh t + h \\ y = b\sinh t + k \\ \end{matrix}
North-south opening hyperbola:
\begin{matrix} x = a\tan t + h \\ y = b\sec t + k \\ \end{matrix} \qquad \mathrm{or} \qquad\begin{matrix} x = a\sinh t + h \\ y = \pm b\cosh t + k \\ \end{matrix}
In all formulae (h,k) are the center coordinates of the hyperbola, a is the length of the semi-major axis, and b is the length of the semi-minor axis.
Posted by at 04:37
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