hyperbole.tex

\documentclass[a4paper]{article}
\usepackage{pst-plot}
\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
 
 
\SpecialCoor
 
\pagestyle{empty}
\begin{document}
Équation :
\[
z=\frac{a}{x-r}
\]
$r$ rayon de l'ouverture supérieure.
\begin{center}
\begin{pspicture}(-1,-1)(10,10)
\psframe(0,0)(8,10)
\psaxes(0,0)(8,10)
\pstVerb{%
         /H 10 def
         /R 8 def
         /r 3 def
         /a H R r sub div def
         /h a R r sub div def
         /x0 a H div r add def}%
\pscustom[linestyle=none]{%
\psline(0,0)(! 0 H)(!x0 H)
\parametricplot{x0}{R}{%
    t
    a t r sub div}%
\psline(! R h)(! R 0)%
    \fill[fillstyle=vlines]}
\parametricplot[linecolor=red,linewidth=2\pslinewidth]{x0}{R}{%
    t
    a t r sub div}%
\end{pspicture}
\end{center}
 
 
\begin{center}
\begin{pspicture}(-1,-1)(10,10)
\psframe(0,0)(8,10)
\psaxes(0,0)(8,10)
\pstVerb{%
         /H 8 def
         /R 4.5 def
         /r 2 def
         /a 5 def
         /xI r a add def
         /theta 1 H R div atan def
         /alpha 90 theta sub def
         /cosT 1 1 H R div dup mul add sqrt div def
         /zI H R div r a add mul neg H add a cosT div add def}%
\pscustom[linestyle=none]{%
\psline(0,0)(! 0 H)(! r H)(!r zI)
\parametricplot{180}{180 theta add}{%
    t
    a t cos mul r add a add
    a t sin mul zI add}%
\psline(! a 180 theta add cos mul r add a add
          a 180 theta add sin mul zI add)(! R 0)%
    \fill[fillstyle=vlines]}
\psset{linecolor=red,linewidth=2\pslinewidth}
\psline(0,0)(! 0 H)(! r H)(!r zI)
\parametricplot{180}{180 theta add}{%
    t
    a t cos mul r add a add
    a t sin mul zI add}%
\psline(! a 180 theta add cos mul r add a add
          a 180 theta add sin mul zI add)(! R 0)(0,0)%
\end{pspicture}
\end{center}
 
\end{document}