# LaTeX2HTML 2002 (1.62)
# Associate images original text with physical files.


$key = q/v_1=displaystylefrac{1}{sqrt2}(1,1);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$v_1=\displaystyle\frac{1}{\sqrt 2}(1,1)$">|; 

$key = q/mathbfR^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$\mathbf R^2$">|; 

$key = q/{displaymath}left{array{{c}xi=X-alphaeta=Y-betaarray{right.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="\begin{displaymath}
\left\{
\begin{array}{c}
\xi=X-\alpha\\\\
\eta=Y-\beta
\end{array}
\right.
\end{displaymath}">|; 

$key = q/includegraphics[width=9cm,height=20cm]{es2iperbole.eps};LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="394" HEIGHT="896" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="\includegraphics[width=9cm,height=20cm]{es2iperbole.eps}">|; 

$key = q/{displaymath}left{array{{c}xi=X-displaystylefrac{3sqrt{2}}{16}eta=Y-displaystylefrac{sqrt{2}}{8}array{right.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="86" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="\begin{displaymath}
\left\{
\begin{array}{c}
\xi=X-\displaystyle\frac{3\sqrt{...
...
\eta=Y-\displaystyle\frac{\sqrt{2}}{8}
\end{array}
\right.
\end{displaymath}">|; 

$key = q/4beta=displaystylefrac{1}{sqrt{2}};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$4\beta=\displaystyle\frac{1}{\sqrt{2}}$">|; 

$key = q/8alpha=displaystylefrac{3}{sqrt{2}};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$8\alpha=\displaystyle\frac{3}{\sqrt{2}}$">|; 

$key = q/lambda_2=-2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$\lambda_2=-2$">|; 

$key = q/q(x,y)=x^2+6xy+y^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$q(x,y)=x^2+6xy+y^2$">|; 

$key = q/4X^2-2Y^2+displaystylefrac{9}{32}=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$4X^2-2Y^2+\displaystyle\frac{9}{32}=0$">|; 

$key = q/x^2+6xy+y^2+2x+y+displaystylefrac{1}{2}=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="245" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$x^2+6xy+y^2+2x+y+\displaystyle\frac{1}{2}=0$">|; 

$key = q/mathcalP=displaystylefrac{1}{sqrt{2}}left(array{{cr}1&-11&1array{right);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$
\mathcal P=\displaystyle\frac{1}{\sqrt{2}} \left(
\begin{array}{cr}
1 &amp; -1\\\\
1 &amp; 1
\end{array}
\right)$">|; 

$key = q/{displaymath}left(array{{c}xyarray{right)=mathcalP^tleft(array{{c}xietaarray{rig}xi+displaystylefrac{1}{sqrt{2}}etaarray{right),{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="311" HEIGHT="98" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="\begin{displaymath}
\left(
\begin{array}{c}
x\ y
\end{array}
\right)=\math...
...xi+\displaystyle\frac{1}{\sqrt{2}}\eta
\end{array}
\right),
\end{displaymath}">|; 

$key = q/p_mathcalA(lambda)=lambda^2-2lambda-8;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$p_\mathcal A(\lambda)=\lambda^2-2\lambda-8$">|; 

$key = q/4xi^2-2eta^2+displaystylefrac{3}{sqrt{2}}xi-displaystylefrac{1}{sqrt{2}}eta+displaystylefrac{1}{2}=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="256" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$4\xi^2-2\eta^2+\displaystyle\frac{3}{\sqrt{2}}\xi-
\displaystyle\frac{1}{\sqrt{2}}\eta+\displaystyle\frac{1}{2}=0$">|; 

$key = q/{displaymath}4X^2-2Y^2+(displaystylefrac{3}{sqrt{2}}-8alpha)X+(-displaystylefraca+displaystylefrac{1}{sqrt{2}}beta+frac{1}{2}=0.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="555" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="\begin{displaymath}
4X^2-2Y^2+(\displaystyle\frac{3}{\sqrt{2}}-8\alpha)X+(-\dis...
...2}}\alpha+\displaystyle\frac{1}{\sqrt{2}}\beta+\frac{1}{2}=0.
\end{displaymath}">|; 

$key = q/1^circ;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$1^\circ$">|; 

$key = q/{displaymath}displaystylefrac{Y^2}{2}-X^2=displaystylefrac{9}{128}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="\begin{displaymath}
\displaystyle\frac{Y^2}{2}-X^2=\displaystyle\frac{9}{128}
\end{displaymath}">|; 

$key = q/v_2=displaystylefrac{1}{sqrt2}(-1,1);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$v_2=\displaystyle\frac{1}{\sqrt 2}(-1,1)$">|; 

$key = q/mathcalA;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$\mathcal A$">|; 

$key = q/mathcalA=left(array{{lr}1&33&1array{right);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$\mathcal
A=\left(
\begin{array}{lr}
1 &amp; 3\\\\
3 &amp; 1
\end{array}
\right)$">|; 

$key = q/lambda_1=4;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$\lambda_1=4$">|; 

1;

