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


$key = q/c>a;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$c&gt;a$">|; 

$key = q/P=(x,y);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$P=(x,y)$">|; 

$key = q/{displaymath}frac{x^{2}}{a^{2}}-frac{y^{2}}{(c^{2}-a^{2})}=1.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="\begin{displaymath}
\frac{x^{2}}{a^{2}}-\frac{y^{2}}{(c^{2}-a^{2})}=1.
\end{displaymath}">|; 

$key = q/{displaymath}x^{2}(1-e^{2})+y^{2}=a^{2}-c^{2}+2cx-2eax{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="295" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="\begin{displaymath}
x^{2}(1-e^{2})+y^{2}=a^{2}-c^{2}+2cx-2eax
\end{displaymath}">|; 

$key = q/displaystylee=frac{c}{a};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$\displaystyle e=\frac{c}{a}$">|; 

$key = q/{displaymath}frac{d(P,F)}{d(P,d)}=e{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="\begin{displaymath}
\frac{d(P,F)}{d(P,d)}=e
\end{displaymath}">|; 

$key = q/{displaymath}(x-c)^{2}+y^{2}=(a-ex)^{2}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="188" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="\begin{displaymath}
(x-c)^{2}+y^{2}=(a-ex)^{2}
\end{displaymath}">|; 

$key = q/displaystyleoverline{FF'}>|overline{PF}-overline{PF'}|;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$\displaystyle\overline{FF'}&gt;\vert\overline{PF}-\overline{PF'}\vert$">|; 

$key = q/x;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$x$">|; 

$key = q/F,F';MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$F, F'$">|; 

$key = q/{displaymath}-a^{2}-xc=asqrt{(x+c)^{2}+y^{2}}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="215" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="\begin{displaymath}
-a^{2}-xc=a\sqrt{(x+c)^{2}+y^{2}}
\end{displaymath}">|; 

$key = q/d(P,F)-d(P,F')=2a;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="183" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$d(P,F)-d(P,F')=2a$">|; 

$key = q/e;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$e$">|; 

$key = q/(O,x,y);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$(O,x,y)$">|; 

$key = q/F',;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$F',$">|; 

$key = q/displaystylex=frac{a}{e};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$\displaystyle x=\frac{a}{e}$">|; 

$key = q/2a;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$2a$">|; 

$key = q/{displaymath}x^{2}(1-e^{2})+y^{2}=2(c-ea)x+a^{2}-c^{2}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="290" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="\begin{displaymath}
x^{2}(1-e^{2})+y^{2}=2(c-ea)x+a^{2}-c^{2}
\end{displaymath}">|; 

$key = q/{displaymath}sqrt{(x-c)^{2}+y^{2}}=2a+sqrt{(x+c)^{2}+y^{2}}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="289" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="\begin{displaymath}
\sqrt{(x-c)^{2}+y^{2}}=2a+ \sqrt{(x+c)^{2}+y^{2}}
\end{displaymath}">|; 

$key = q/(pmc,0);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$(\pm c,0)$">|; 

$key = q/{displaymath}(x-c)^{2}-(x+c)^{2}=4a^{2}+4asqrt{(x+c)^{2}+y^{2}}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="342" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="\begin{displaymath}
(x-c)^{2}-(x+c)^{2}=4a^{2}+4a\sqrt{(x+c)^{2}+y^{2}}
\end{displaymath}">|; 

$key = q/overrightarrow{FF'};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="22" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$\overrightarrow{FF'}$">|; 

$key = q/F;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$F$">|; 

$key = q/{displaymath}frac{sqrt{(x-c)^{2}+y^{2}}}{displaystyle|frac{a}{e}-x|}=e{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="63" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="\begin{displaymath}
\frac{\sqrt{(x-c)^{2}+y^{2}}}{ \displaystyle\vert\frac{a}{e}-x\vert}=e
\end{displaymath}">|; 

$key = q/displaystylesqrt{(x+c)^{2}+y^{2}}-sqrt{(x-c)^{2}+y^{2}}=2a;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="295" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$\displaystyle\sqrt{(x+c)^{2}+y^{2}}-\sqrt{(x-c)^{2}+y^{2}}=2a$">|; 

$key = q/includegraphics[width=9cm,height=7.5cm]{i-l_geom};LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="408" HEIGHT="339" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="\includegraphics[width=9cm,height=7.5cm]{i-l_geom}">|; 

$key = q/{displaymath}x^{2}(c^{2}-a^{2})-a^{2}y^{2}=a^{2}(c^{2}-a^{2}){displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="244" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="\begin{displaymath}
x^{2}(c^{2}-a^{2})-a^{2}y^{2}=a^{2}(c^{2}-a^{2})
\end{displaymath}">|; 

$key = q/P;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$P$">|; 

$key = q/2c>2a;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$2c&gt;2a$">|; 

$key = q/{displaymath}x^{2}c^{2}+a^{4}+2a^{2}xc=a^{2}(x^{2}+c^{2}+2xc+y^{2}){displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="326" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="\begin{displaymath}
x^{2}c^{2}+a^{4}+2a^{2}xc=a^{2}(x^{2}+c^{2}+2xc+y^{2})
\end{displaymath}">|; 

$key = q/{displaymath}-4xc=4a^{2}+4asqrt{(x+c)^{2}+y^{2}}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="241" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="\begin{displaymath}
-4xc=4a^{2}+4a\sqrt{(x+c)^{2}+y^{2}}
\end{displaymath}">|; 

$key = q/FF'P;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$FF'P$">|; 

$key = q/b^{2}=c^{2}-a^{2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$b^{2}=c^{2}-a^{2}$">|; 

$key = q/overline{FF'};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$\overline{FF'}$">|; 

$key = q/F=(c,0);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$F=(c,0)$">|; 

$key = q/P(x,y);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="$P(x,y)$">|; 

1;

