



\def{integer a=randint(2..7)}
\def{integer b = randint(2..7)}
\def{fraction p = \b/\a}
\def{integer c=max(\a,\b)}
\def{integer B=\b^2}
\def{integer A=\a^2}
\def{integer C=2*\p}
\def{integer epsilon=randint(-1,1)}
\def{real d=sqrt(\b/\a)}

\def{text hyperbole1=
xrange -2*\c,2*\c
yrange -2*\c,2*\c
levelcurve red,x^2/\a^2-y^2/\b^2, 1
hline 0,0, black
vline 0,0, black
arrow 0,0,1,0,8, black
arrow 0,0,0,1,8, black
}

\def{text hyperbole2=
xrange -2*\c,2*\c
yrange -2*\c,2*\c
levelcurve red,y^2/\b^2-x^2/\a^2, 1
hline 0,0, black
vline 0,0, black
arrow 0,0,1,0,8, black
arrow 0,0,0,1,8, black
}


\def{text droites=
xrange -2*\c,2*\c
yrange -2*\c,2*\c
plot red,-sqrt((\b/\a))*x 
plot red, sqrt((\b/\a))*x
fcircle 0,0,6, black
copy 0.3,0.3,-1,-1,-1,-1,mathfonts/109/omega.gif
}


<table cellpadding="2" cellspacing="2" border="2"
 style="text-align: left; "width: 100%" >
  <tbody>
    <tr>
      <td
 style="vertical-align: top; background-color: rgb(255, 255, 255);"><br>
      <br>
      <br>
\(\lambda h &gt; 0)  </td>
      <td
 style="vertical-align: top; background-color: rgb(255, 204, 255);">\(\mathcal{C})
est une hyperbole d'&eacute;quation
&nbsp;\(\frac{x^2} {a^2} -\frac{y^2}{b^2} -1= 0), de centre
\(\omega) et &nbsp;d'axes \((\omega, \vec{v_1})) et
&nbsp;\((\omega, \vec{v_2}).)</td>
      <td
 style="vertical-align: top; background-color: rgb(255, 255, 255);">\draw{200,200}{
\hyperbole1
}
     
Hyperbole d'&eacute;quation : \(\frac{x^2} {\A}
-\frac{y^2}{\B} = 1.) <br>
      </td>
    </tr>
    <tr>
      <td
 style="vertical-align: top; background-color: rgb(255, 255, 255);">
<br>
\(h = 0)</td>
      <td
 style="vertical-align: top; background-color: rgb(204, 204, 255);">\(\mathcal{C})
est la r&eacute;union de deux
droites passant par &nbsp;\(omega) et d'&eacute;quations \(y=
\pm\sqrt{-\frac{\lambda}{\mu}}x.)</td>
      <td style="vertical-align: top;">
      <table style="text-align: left; "width: 100%"; 
 border="2" cellpadding="2" cellspacing="2">
        <tbody>
          <tr>
            <td>
\draw{200,200}{\droites
}
R&eacute;union de deux droites d'&eacute;quations:
\(y = -\p x  et  y = \p x)

            </td>
          </tr>
        </tbody>
      </table>
      </td>
    </tr>
    <tr>
      <td
 style="vertical-align: top; background-color: rgb(255, 255, 255);"><br>
      <br>
      <br>
\(\lambda h &lt; 0)</td>
      <td
 style="vertical-align: top; background-color: rgb(204, 255, 255);">\(\mathcal{C})
est une hyperbole d'&eacute;quation
&nbsp;\(\frac{y^2} {a^2} -\frac{x^2}{b^2} -1= 0), de centre
\(\omega) et &nbsp;d'axes \((\omega, \vec{v_1})) et
&nbsp;\((\omega, \vec{v_2}).)</td>
      <td style="vertical-align: top;">\draw{200,200}{
\hyperbole2
}
Hyperbole d'&eacute;quation : \(\frac{y^2} {\A}
-\frac{x^2}{\B} = 1.) 
      </td>
    </tr>
  </tbody>
</table>

<a name="exemple11">

\reload{Renouvelez les figures}{exemple11}


