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


$key = q/displaystyley=-frac{b}{a}x;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$\displaystyle y=-\frac{b}{a}x$">|; 

$key = q/{displaymath}lim_{xrightarrow+infty}(frac{b}{a}sqrt{x^{2}-a^{2}}-frac{b}{a}x)=lihtarrow+infty}(frac{b}{a}(sqrt{x^{2}-a^{2}}-x))={displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="417" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="\begin{displaymath}
\lim_{x \rightarrow
+\infty}(\frac{b}{a}\sqrt{x^{2}-a^{2}}...
..._{x
\rightarrow +\infty}(\frac{b}{a}(\sqrt{x^{2}-a^{2}}-x))=
\end{displaymath}">|; 

$key = q/X=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$X=0$">|; 

$key = q/xy=c;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="$xy=c$">|; 

$key = q/{displaymath}left{array{{rl}X=xcostheta-ysinthetaY=xsintheta+ycosthetaarray{right.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="\begin{displaymath}
\left \{
\begin{array}{rl}
X=x\cos\theta-y\sin\theta\\\\
Y=x\sin\theta+y\cos\theta
\end{array}
\right.
\end{displaymath}">|; 

$key = q/xrightarrow-infty;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$x\rightarrow -\infty$">|; 

$key = q/X=p;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$X=p$">|; 

$key = q/displaystyley=pm(frac{b}{a})x;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$\displaystyle y=\pm(\frac{b}{a})x$">|; 

$key = q/{displaymath}frac{(x-1)^{2}}{(sqrt{2})^{2}}-frac{(y-2)^{2}}{(sqrt{6})^{2}}=1.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="\begin{displaymath}
\frac{(x-1)^{2}}{(\sqrt{2})^{2}}-\frac{(y-2)^{2}}{(\sqrt{6})^{2}}=1.
\end{displaymath}">|; 

$key = q/Y=pmsqrt{3}X;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$Y=\pm\sqrt{3}X$">|; 

$key = q/{displaymath}frac{(X)^{2}}{(sqrt{2})^{2}}-frac{(Y)^{2}}{(sqrt{6})^2}=1.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="\begin{displaymath}
\frac{(X)^{2}}{(\sqrt{2})^{2}}-\frac{(Y)^{2}}{(\sqrt{6})^2}=1.
\end{displaymath}">|; 

$key = q/mathcal{C}:X^{2}-Y^{2}=a^{2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="$\mathcal{C}: X^{2}-Y^{2}=a^{2}$">|; 

$key = q/{displaymath}displaystylexy=frac{1}{2}a^{2}qquad(con,,frac{a^2}{2}>0).{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="209" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="\begin{displaymath}
\displaystyle xy=\frac{1}{2}a^{2}\qquad (con    
\frac{a^2}{2}&gt;0).
\end{displaymath}">|; 

$key = q/{displaymath}lim_{xrightarrow+infty}(frac{b}{a},frac{(sqrt{x^{2}-a^{2}}-x)(sqrt{x^{2}-a^{2}}+x)}{sqrt{x^{2}-a^{2}}+x})={displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="326" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="\begin{displaymath}
\lim_{x \rightarrow +\infty}(\frac{b}{a}   \frac{(
\sqrt{x^{2}-a^{2}}-x)(\sqrt{x^{2}-a^{2}}+x)}{\sqrt{x^{2}-a^{2}}+x})=
\end{displaymath}">|; 

$key = q/Y=q;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$Y=q$">|; 

$key = q/(1,2);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="$(1,2)$">|; 

$key = q/includegraphics[width=9cm,height=7.5cm]{i-asintoti};LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="408" HEIGHT="340" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="\includegraphics[width=9cm,height=7.5cm]{i-asintoti}">|; 

$key = q/xrightarrow+infty;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$x\rightarrow+\infty$">|; 

$key = q/a=b;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$a=b$">|; 

$key = q/X,Y;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$X,Y$">|; 

$key = q/displaystyle3x^2-y^2-6x+4y-7=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$\displaystyle 3x^2-y^2-6x+4y-7=0$">|; 

$key = q/x,y;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="$x, y$">|; 

$key = q/displaystyley=-frac{b}{a}sqrt{x^{2}-a^{2}};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$\displaystyle y=-\frac{b}{a}\sqrt{x^{2}-a^{2}}$">|; 

$key = q/[q,+infty).;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$[q,+\infty).$">|; 

$key = q/x=1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="$x=1$">|; 

$key = q/f(x);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$f(x)$">|; 

$key = q/y=ax+b;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$y=ax+b$">|; 

$key = q/displaystyletheta=-frac{pi}{4};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="$\displaystyle\theta=-\frac{\pi}{4}$">|; 

$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|img17.png"
 ALT="$2a$">|; 

$key = q/y=pmx;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="$y=\pm x$">|; 

$key = q/y=2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="$y=2$">|; 

$key = q/{displaymath}3(x-1)^{2}-(y^{2}-4y+4)-10+4=0{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="291" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="\begin{displaymath}
3(x-1)^{2}-(y^{2}-4y+4)-10+4=0
\end{displaymath}">|; 

$key = q/F=(pm2sqrt{2},0);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$F=(\pm2\sqrt{2},0)$">|; 

$key = q/includegraphics[width=9cm,height=7.5cm]{ipequilatera};LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="408" HEIGHT="339" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="\includegraphics[width=9cm,height=7.5cm]{ipequilatera}">|; 

$key = q/{displaymath}lim_{xrightarrow+infty}{(f(x)-ax-b)}=0.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="\begin{displaymath}
\lim_{x \rightarrow +\infty}{(f(x)-ax-b)}=0.
\end{displaymath}">|; 

$key = q/{displaymath}3(x^{2}-2x+1)-y^{2}+4y-7-3=0{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="278" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="\begin{displaymath}
3(x^{2}-2x+1)-y^{2}+4y-7-3=0
\end{displaymath}">|; 

$key = q/A=(pmsqrt{2},0).;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="$A=(\pm\sqrt{2},0).$">|; 

$key = q/c>0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="$c&gt;0$">|; 

$key = q/displaystylefrac{(x-p)^{2}}{a^{2}}+frac{(y-q)^{2}}{b^{2}}=1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$\displaystyle\frac{(x-p)^{2}}{a^{2}}+\frac{(y-q)^{2}}{b^{2}}=1$">|; 

$key = q/a,b;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$a, b$">|; 

$key = q/{displaymath}lim_{xrightarrow+infty}(frac{b}{a},frac{(x^{2}-a^{2}-x^{2})}{sqrt{xhtarrow+infty}(frac{-ab}{sqrt{x^{2}-a^{2}}+x})=0{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="405" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="\begin{displaymath}
\lim_{x \rightarrow +\infty}(\frac{b}{a}   \frac{(x^{2}
-...
..._{x \rightarrow
+\infty}(\frac{-ab}{\sqrt{x^{2}-a^{2}}+x})=0
\end{displaymath}">|; 

$key = q/{displaymath}left{array{{rl}X=displaystylefrac{sqrt{2}}{2}(x+y)Y=displaystylefrac{sqrt{2}}{2}(-x+y)array{right.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="86" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="\begin{displaymath}
\left \{
\begin{array}{rl}
X=\displaystyle\frac{\sqrt{2}}...
...Y=\displaystyle\frac{\sqrt{2}}{2}(-x+y)
\end{array}
\right.
\end{displaymath}">|; 

$key = q/(0,0);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="$(0,0)$">|; 

$key = q/C=(p,q);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$C=(p,q)$">|; 

$key = q/A=(pmsqrt{2}+1,2).;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="$A=(\pm\sqrt{2}+1,2).$">|; 

$key = q/{displaymath}left{array{{l}X=x-1Y=y-2array{right.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="\begin{displaymath}
\left \{
\begin{array}{l}
X=x-1\\\\
Y=y-2\\\\
\end{array}
\right.
\end{displaymath}">|; 

$key = q/2b;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$2b$">|; 

$key = q/{displaymath}displaystylefrac{1}{2}(x+y)^{2}-frac{1}{2}(-x+y)^{2}=a^{2}{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="\begin{displaymath}
\displaystyle\frac{1}{2}(x+y)^{2}-\frac{1}{2}(-x+y)^{2}=a^{2}
\end{displaymath}">|; 

$key = q/displaystylefrac{X^{2}}{a^{2}}-frac{Y^{2}}{a^2}=1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="$\displaystyle\frac{X^{2}}{a^{2}}-\frac{Y^{2}}{a^2}=1$">|; 

$key = q/{displaymath}3(x-1)^{2}-(y-2)^{2}=6{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="183" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="\begin{displaymath}
3(x-1)^{2}-(y-2)^{2}=6
\end{displaymath}">|; 

$key = q/{displaymath}left{array{{l}X=x-p,Y=y-qarray{right.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="\begin{displaymath}
\left \{
\begin{array}{l}
X=x-p\\\\
 
Y=y-q\\\\
\end{array}
\right.
\end{displaymath}">|; 

$key = q/Y=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$Y=0$">|; 

$key = q/mathcal{C};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$\mathcal{C}$">|; 

$key = q/(y-2)=pmsqrt{3}(x-1);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="171" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$(y-2)=\pm\sqrt{3}(x-1)$">|; 

$key = q/F=(pm2sqrt{2}+1,2);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="$F=(\pm2\sqrt{2}+1,2)$">|; 

1;

