Editing Parametric equation (section)

===Hyperbola===
An east-west opening [[hyperbola]] can be represented parametrically by

<math display="block">\begin{align}
  x &= a\sec t + h \\
  y &= b\tan t + k\,,
\end{align}</math>

or, [[rational function|rationally]]

<math display="block">\begin{align}
  x &= a\frac{1 + t^2}{1 - t^2} + h \\
  y &= b\frac{2t}{1 - t^2}  + k\,.
\end{align}</math>

A north-south opening hyperbola can be represented parametrically as

<math display="block">\begin{align}
  x &= b\tan t + h \\
  y &= a\sec t + k\,,
\end{align}</math>

or, rationally

<math display="block">\begin{align}
  x &= b\frac{2t}{1 - t^2} + h \\
  y &= a\frac{1 + t^2}{1 - t^2} + k\,.
\end{align}</math>

In all these formulae {{math|(''h'' , ''k'')}} are the center coordinates of the hyperbola, {{mvar|a}} is the length of the semi-major axis, and {{mvar|b}} is the length of the semi-minor axis. Note that in the rational forms of these formulae, the points {{math|(''−a'' , 0)}} and {{math|(0 , ''−a'')}}, respectively, are not represented by a real value of {{mvar|t}}, but are the limit of {{mvar|x}} and {{mvar|y}} as {{mvar|t}} tends to infinity.