hyperbola - Maple Help

plottools

 hyperbola
 generate 2-D plot object for a hyperbola

 Calling Sequence hyperbola(c, a, b, r, options)

Parameters

 c - center of symmetry a, b - a^2+b^2=e^2, where e is the eccentricity r - range options - (optional) equations of the form option=value. For a complete list, see plot/options.

Description

 • 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

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

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

Examples

 > $\mathrm{with}\left(\mathrm{plottools}\right):$
 > $\mathrm{with}\left(\mathrm{plots}\right):$
 > $\mathrm{eq}≔\frac{{\left(x-\mathrm{x0}\right)}^{2}}{{a}^{2}}-\frac{{\left(y-\mathrm{y0}\right)}^{2}}{{b}^{2}}=1$
 ${\mathrm{eq}}{≔}\frac{{\left({x}{-}{\mathrm{x0}}\right)}^{{2}}}{{{a}}^{{2}}}{-}\frac{{\left({y}{-}{\mathrm{y0}}\right)}^{{2}}}{{{b}}^{{2}}}{=}{1}$ (1)
 > $a≔1:$$b≔1:$$\mathrm{x0}≔0:$$\mathrm{y0}≔0:$

Generate the hyperbola described by the equation above,

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

which is equivalent to:

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

Other forms of hyperbola can be obtained via object transformations, for example, rotate.

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