Pages

Subscribe:

Labels

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.

0 comments:

Post a Comment