# LaTeX2HTML 99.1 release (March 30, 1999)
# Associate images original text with physical files.


$key = q/qquadx^2=0qquad;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="img12.gif"
 ALT="$ \qquad x^2=0\qquad$">|; 

$key = q/displaystylebeta_1:frac{textstylex}{textstylea_1}+frac{textstyley}{textstylea_2}c{textstylex}{textstylea_1}-frac{textstyley}{textstylea_2}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="353" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="img7.gif"
 ALT="$\displaystyle \beta_1:\frac{\textstyle x}{\textstyle a_1}+\frac{\textstyle
y}{...
...2:\frac{\textstyle
x}{\textstyle a_1}-\frac{\textstyle y}{\textstyle a_2}=0.
$">|; 

$key = q/displaystylefrac{textstylex^2}{textstylea_1^2}+1=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="img11.gif"
 ALT="$\displaystyle \frac{\textstyle x^2}{\textstyle
a_1^2}+1=0
$">|; 

$key = q/displaystylefrac{textstylex^2}{textstylea_1^2}+frac{textstyley^2}{textstylea_2^2}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="img1.gif"
 ALT="$\displaystyle \frac{\textstyle x^2}{\textstyle a_1^2}+\frac{\textstyle
y^2}{\textstyle a_2^2}=0
$">|; 

$key = q/displaystylefrac{textstylex^2}{textstylea_1^2}-frac{textstyley^2}{textstylea_2^2}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="img5.gif"
 ALT="$\displaystyle \frac{\textstyle x^2}{\textstyle a_1^2}-\frac{\textstyle
y^2}{\textstyle a_2^2}=0
$">|; 

$key = q/,z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="img2.gif"
 ALT="$ \,z$">|; 

$key = q/displaystylegamma_1:frac{textstylex}{textstylea_1}+ifrac{textstyley}{textstylea_{textstylex}{textstylea_1}-ifrac{textstyley}{textstylea_2}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="364" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="img4.gif"
 ALT="$\displaystyle \gamma_1:\frac{\textstyle x}{\textstyle a_1}+i\frac{\textstyle
y...
...:\frac{\textstyle
x}{\textstyle a_1}-i\frac{\textstyle y}{\textstyle a_2}=0.
$">|; 

$key = q/displaystylebeta_1:x=sqrt{a_1}qquadqquadbeta_2:x=-sqrt{a_1}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="306" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img10.gif"
 ALT="$\displaystyle \beta_1:x=\sqrt{a_1}\qquad\qquad \beta_2:x=-\sqrt{a_1}. $">|; 

$key = q/displaystylefrac{textstylex^2}{textstylea_1^2}-frac{textstyley^2}{textstylea_2^2tstylex}{textstylea_1}-frac{textstyley}{textstylea_2}right)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="321" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="img6.gif"
 ALT="$\displaystyle \frac{\textstyle x^2}{\textstyle a_1^2}-\frac{\textstyle
y^2}{\t...
...c{\textstyle x}{\textstyle a_1}-\frac{\textstyle
y}{\textstyle a_2}\right)=0
$">|; 

$key = q/,a_1>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img9.gif"
 ALT="$ \,a_1&gt;0$">|; 

$key = q/displaystylefrac{textstylex^2}{textstylea_1^2}-1=0qquad(Rightarrowx^2=a_1^2,);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="234" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="img8.gif"
 ALT="$\displaystyle \frac{\textstyle x^2}{\textstyle a_1^2}-1=0 \qquad (\Rightarrow
x^2 = a_1^2\,)
$">|; 

$key = q/displaystylefrac{textstylex^2}{textstylea_1^2}+frac{textstyley^2}{textstylea_2^2stylex}{textstylea_1}-ifrac{textstyley}{textstylea_2}right)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="334" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="img3.gif"
 ALT="$\displaystyle \frac{\textstyle x^2}{\textstyle a_1^2}+\frac{\textstyle
y^2}{\t...
...{\textstyle x}{\textstyle a_1}-i\frac{\textstyle
y}{\textstyle a_2}\right)=0
$">|; 

$key = q/;x=0;;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="img13.gif"
 ALT="$ \;x=0\;$">|; 

1;

