The hyperbola command creates a two-dimensional plot data object, which when displayed is a hyperbola whose center of symmetry is at point c, with $a^2+b^2=e^2$, where $e$ is the eccentricity. For instance, hyperbola([x0, y0], a, b, r1..r2) graphs the equation

from the point $\left[\mathrm{x0}+a\cosh \left(\mathrm{r1}\right)\,\mathrm{y0}+b\sinh \left(\mathrm{r1}\right)\right]$ to $\left[\mathrm{x0}+a\cosh \left(\mathrm{r2}\right)\,\mathrm{y0}+b\sinh \left(\mathrm{r2}\right)\right]$ and from $\left[\mathrm{x0}-a\cosh \left(\mathrm{r1}\right)\,\mathrm{y0}-b\sinh \left(\mathrm{r1}\right)\right]$ to $\left[\mathrm{x0}-a\cosh \left(\mathrm{r2}\right)\,\mathrm{y0}-b\sinh \left(\mathrm{r2}\right)\right]$.

A call to hyperbola produces a plot data object that can be used in a PLOT data structure, or displayed using the plots[display] command.

Remaining arguments are interpreted as options, which are specified as equations of the form option = value. For more information, see plottools and plot/options.

$\mathrm{with}\left(\mathrm{plottools}\right)\:$

$\mathrm{with}\left(\mathrm{plots}\right)\:$

$\mathrm{eq}≔\frac{{\left(x-\mathrm{x0}\right)}^2}{a^2}-\frac{{\left(y-\mathrm{y0}\right)}^2}{b^2}=1$

$\mathrm{eq}≔\frac{{\left(x-\mathrm{x0}\right)}^2}{a^2}-\frac{{\left(y-\mathrm{y0}\right)}^2}{b^2}=1$

$a≔1\:$$b≔1\:$$\mathrm{x0}≔0\:$$\mathrm{y0}≔0\:$

$h≔\mathrm{hyperbola}\left(\left[\mathrm{x0}\,\mathrm{y0}\right]\,a\,b\,-2..2\right)\:$

$\mathrm{display}\left(h\right)$

$\mathrm{implicitplot}\left(\mathrm{eq}\,x=-4..4\,y=-4..4\right)$

$\mathrm{display}\left(\mathrm{rotate}\left(h\,\frac{\mathrm{\pi }}{2}\right)\,\mathrm{rotate}\left(h\,\frac{\mathrm{\pi }}{4}\right)\,\mathrm{rotate}\left(h\,\frac{3\mathrm{\pi }}{4}\right)\right)$