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


$key = q/b=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$b=0$">|; 

$key = q/{displaymath}lambda_1X^2+d=0{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="\begin{displaymath}
\lambda_1X^2+d=0
\end{displaymath}">|; 

$key = q/a;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$a$">|; 

$key = q/b_{23}=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$b_{23}=0$">|; 

$key = q/{displaymath}d=lambda_1a^2+lambda_2b^2-2b_{13}a-2b_{23}b+b_{33}.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="279" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="\begin{displaymath}
d=\lambda_1a^2+\lambda_2b^2-2b_{13}a-2b_{23}b+b_{33}.
\end{displaymath}">|; 

$key = q/lambda_2=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$\lambda_2=0$">|; 

$key = q/lambda_2neq0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$\lambda_2\neq 0$">|; 

$key = q/lambda_1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$\lambda_1$">|; 

$key = q/c;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$c$">|; 

$key = q/a=displaystylefrac{b_{13}}{lambda_1};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$a=\displaystyle\frac{b_{13}}{\lambda_1}$">|; 

$key = q/lambda_1neq0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$\lambda_1\neq 0$">|; 

$key = q/lambda_1=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$\lambda_1=0$">|; 

$key = q/{displaymath}lambda_1X^2+2b_{23}Y=0{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="\begin{displaymath}
\lambda_1X^2+2b_{23}Y=0
\end{displaymath}">|; 

$key = q/b;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$b$">|; 

$key = q/b=displaystylefrac{b_{23}}{lambda_2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$b=\displaystyle\frac{b_{23}}{\lambda_2}$">|; 

$key = q/{displaymath}lambda_1X^2+lambda_2Y^2+c=0{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="\begin{displaymath}
\lambda_1X^2+\lambda_2Y^2+c=0
\end{displaymath}">|; 

$key = q/{displaymath}left{array{{c}x'=X-ay'=Y-barray{right.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="\begin{displaymath}
\left\{
\begin{array}{c}
x'=X-a\\\\
y'=Y-b
\end{array}
\right.
\end{displaymath}">|; 

$key = q/d=-displaystylefrac{b^2_{13}}{lambda_1}-2b_{23}b+b_{33};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$d=-\displaystyle\frac{b^2_{13}}{\lambda_1}-2b_{23}b+b_{33}$">|; 

$key = q/lambda_2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$\lambda_2$">|; 

$key = q/b_{23}neq0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$b_{23}\neq 0$">|; 

$key = q/{displaymath}lambda_1X^2+lambda_2Y^2+2(b_{13}-lambda_1a)X+2(b_{23}-lambda_2b)Y+d=0{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="418" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="\begin{displaymath}
\lambda_1X^2+\lambda_2Y^2+2(b_{13}-\lambda_1a)X+2(b_{23}-\lambda_2b)Y+d=0
\end{displaymath}">|; 

1;

