# LaTeX2HTML 99.1 release (March 30, 1999)
# Associate images original text with physical files.


$key = q/;a_1,,a_2,,a_3;;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img21.gif"
 ALT="$ \;a_1,\,a_2,\,a_3\;$">|; 

$key = q/,VP,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="img6.gif"
 ALT="$ \,VP\,$">|; 

$key = q/,h,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="img25.gif"
 ALT="$ \,h\,$">|; 

$key = q/,PneqV,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img4.gif"
 ALT="$ \,P \neq V\, $">|; 

$key = q/,K,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="img1.gif"
 ALT="$ \,K\,$">|; 

$key = q/quadx=x_0t,;y=y_0t,;z=z_0t;;;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="238" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img16.gif"
 ALT="$ \quad x=x_0t,\;y=y_0t,\;z=z_0t
\;\;$">|; 

$key = q/,>,0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img22.gif"
 ALT="$ \,&gt;\,0$">|; 

$key = q/,r=OP,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="img14.gif"
 ALT="$ \,r =
OP\,$">|; 

$key = q/;;f(x_0t,y_0t,z_0t)=t^2f(x_0,y_0,z_0)=t^2cdot0=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="359" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="img17.gif"
 ALT="$ \;\;f(x_0t,y_0t,z_0t) = t^2f(x_0,y_0,z_0)= t^2 \cdot
0=0$">|; 

$key = q/,r,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="img15.gif"
 ALT="$ \,r\,$">|; 

$key = q/;f(x_0,y_0,z_0)=0;;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img13.gif"
 ALT="$ \;f(x_0,y_0,z_0)=0\;$">|; 

$key = q/,S,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="img3.gif"
 ALT="$ \,S\,$">|; 

$key = q/,a,,b,,c,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img18.gif"
 ALT="$ \,a,\,b,\,c\,$">|; 

$key = q/,V,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="img2.gif"
 ALT="$ \,V\,$">|; 

$key = q/qquadax^2+by^2+cz^2=0qquad(a,,b,,c,neq0)quad;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="358" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="img10.gif"
 ALT="$ \qquad ax^2 + by^2 + cz^2 = 0 \qquad
(a,\,b,\,c\,\neq 0)\quad$">|; 

$key = q/,f(x,y,z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img7.gif"
 ALT="$ \,f(x,y,z)\,$">|; 

$key = q/;f(tx,ty,tz)=t^{textit{k}}f(x,y,z);;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="img8.gif"
 ALT="$ \;f(tx,ty,tz) =
t^{\textit{k}}f(x,y,z)\;$">|; 

$key = q/displaystylefrac{textstylex^2}{textstylea_1^2}+frac{textstyley^2}{textstylea_2^2}+frac{textstylez^2}{textstylea_3^2}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="img20.gif"
 ALT="$\displaystyle \frac{\textstyle x^2}{\textstyle a_1^2}+\frac{\textstyle
y^2}{\textstyle a_2^2} +\frac{\textstyle z^2}{\textstyle a_3^2}=0
$">|; 

$key = q/,t,,x,,y,,z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img9.gif"
 ALT="$ \,t,\,x,\,y,\,z$">|; 

$key = q/;z=h;;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="img24.gif"
 ALT="$ \;z=h\;$">|; 

$key = q/displaystylefrac{textstylex^2}{textstylea_1^2}+frac{textstyley^2}{textstylea_2^2}-frac{textstylez^2}{textstylea_3^2}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="img23.gif"
 ALT="$\displaystyle \frac{\textstyle x^2}{\textstyle a_1^2}+\frac{\textstyle
y^2}{\textstyle a_2^2} -\frac{\textstyle z^2}{\textstyle a_3^2}=0
$">|; 

$key = q/,K;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="img5.gif"
 ALT="$ \,K$">|; 

$key = q/,O;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="img11.gif"
 ALT="$ \,O$">|; 

$key = q/;P(x_0,y_0,z_0)neq0;;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img12.gif"
 ALT="$ \;P(x_0,y_0,z_0) \neq 0
\;$">|; 

$key = q/,mathcal{Q},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img19.gif"
 ALT="$ \,\mathcal{Q} \,$">|; 

1;

