document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1133039>Question 1133039</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hallar la ecuacion de las hiperbolas determinadas por:<BR>\n" );
document.write( "1) vertices (+-1,0) asíntotas y=+-5x<BR>\n" );
document.write( "2) focos (0,+-6) pasa por P=(-5,9)<BR>\n" );
document.write( "3) focos (0,+-1) longitud eje real:1<BR>\n" );
document.write( "4) asíntotas y= +- x/2 pasa por el punto de coordenadas (5,2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #750212 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=750212\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Standard form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >->Transverse axis is horizontal\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-h%29%5E2%2Fa%5E2-%28x-k%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28y-h%29%5E2%2Fa%5E2-%28x-k%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >-.>Transverse axis is vertical\r<BR>\n" );
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document.write( "1) \r<BR>\n" );
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document.write( "given:\r<BR>\n" );
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document.write( "Vertices: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >), (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >) =>Semi-major axis length: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=6 ALIGN=MIDDLE  ALT=\"a=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2F6%5E2-%28y-k%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2F6%5E2-%28y-k%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2F36-%28y-k%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2F36-%28y-k%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "First asymptote: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5x ALIGN=MIDDLE  ALT=\"y=-5x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Second asymptote: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5x ALIGN=MIDDLE  ALT=\"y=5x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=> Transverse axis is vertical\r<BR>\n" );
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document.write( "Standard form: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-h%29%5E2%2Fa%5E2-%28x-k%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28y-h%29%5E2%2Fa%5E2-%28x-k%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "intersection of the asymptotes is at origin: \r<BR>\n" );
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document.write( "so, center is at: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=0+ ALIGN=MIDDLE  ALT=\"h=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=0 ALIGN=MIDDLE  ALT=\"k=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2Fa%5E2-x%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"y%5E2%2Fa%5E2-x%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "From the original equations of asymptotes, you can determine the slopes of the asymptotes to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=5 ALIGN=MIDDLE  ALT=\"m=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-5 ALIGN=MIDDLE  ALT=\"m=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=a%2Fb ALIGN=MIDDLE  ALT=\"m=a%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=6 ALIGN=MIDDLE  ALT=\"a=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=6%2Fb ALIGN=MIDDLE  ALT=\"5=6%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=6%2F5 ALIGN=MIDDLE  ALT=\"b=6%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F36-y%5E2%2F%286%2F5%29%5E2=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F36-y%5E2%2F%286%2F5%29%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F36-y%5E2%2F%2836%2F25%29=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F36-y%5E2%2F%2836%2F25%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F36-25y%5E2%2F36=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F36-25y%5E2%2F36=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2.  \r<BR>\n" );
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document.write( "2) focos (0,+-6) pasa por P=(-5,9)\r<BR>\n" );
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document.write( "the coordinates of the foci are (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,±<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "foci lie on y axis, so your formula is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2Fa%5E2-x%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"y%5E2%2Fa%5E2-x%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=6 ALIGN=MIDDLE  ALT=\"c=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-6 ALIGN=MIDDLE  ALT=\"c=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%5E2=a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"6%5E2=a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36=a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"36=a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=36-a%5E2 ALIGN=MIDDLE  ALT=\"b%5E2=36-a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " P=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( " <TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=formula_distance.solver>Distance Between 2 points</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>The distance formula is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Plug in the numbers,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28%28-5-%280%29%29%5E2%29%2B%28%289-%28-6%29%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28%28-5-%280%29%29%5E2%29%2B%28%289-%28-6%29%29%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-5%5E2%2B15%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28-5%5E2%2B15%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  The distance is 15.8113883008419.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D=15.8113883008419 ALIGN=MIDDLE  ALT=\"d%5B1%5D=15.8113883008419\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> round it to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D=16 ALIGN=MIDDLE  ALT=\"d%5B1%5D=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=formula_distance.solver>Distance Between 2 points</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>The distance formula is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Plug in the numbers,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28%28-5-%280%29%29%5E2%29%2B%28%289-%286%29%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28%28-5-%280%29%29%5E2%29%2B%28%289-%286%29%29%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-5%5E2%2B3%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28-5%5E2%2B3%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  The distance is 5.8309518948453.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D=5.8309518948453 ALIGN=MIDDLE  ALT=\"d%5B2%5D=5.8309518948453\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> round it to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D=6 ALIGN=MIDDLE  ALT=\"d%5B2%5D=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a=16-6=10 ALIGN=MIDDLE  ALT=\"2a=16-6=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=10%2F2=5 ALIGN=MIDDLE  ALT=\"a=10%2F2=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=36-5%5E2 ALIGN=MIDDLE  ALT=\"b%5E2=36-5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=36-25 ALIGN=MIDDLE  ALT=\"b%5E2=36-25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+=+11 ALIGN=MIDDLE  ALT=\"b%5E2+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2F25-x%5E2%2F11=1 ALIGN=MIDDLE  ALT=\"y%5E2%2F25-x%5E2%2F11=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "3) focos (0,+-1) longitud eje real:1\r<BR>\n" );
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document.write( "longitud eje real:1=> the length transverse axis is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a=1 ALIGN=MIDDLE  ALT=\"2a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1%2F2 ALIGN=MIDDLE  ALT=\"a=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the coordinates of the foci are (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,±<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >) => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >=±<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and\r<BR>\n" );
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document.write( "foci lie on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > axis, so your formula is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2Fa%5E2-x%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"y%5E2%2Fa%5E2-x%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=1 ALIGN=MIDDLE  ALT=\"c=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-1 ALIGN=MIDDLE  ALT=\"c=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%5E2=%281%2F2%29%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"1%5E2=%281%2F2%29%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=1%2F4%2Bb%5E2 ALIGN=MIDDLE  ALT=\"1=1%2F4%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=1-1%2F4 ALIGN=MIDDLE  ALT=\"b%5E2=1-1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=3%2F4 ALIGN=MIDDLE  ALT=\"b%5E2=3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2F%281%2F4%29-x%5E2%2F%283%2F4%29=1 ALIGN=MIDDLE  ALT=\"y%5E2%2F%281%2F4%29-x%5E2%2F%283%2F4%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%5E2-4x%5E2%2F3=1 ALIGN=MIDDLE  ALT=\"4y%5E2-4x%5E2%2F3=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "4) asíntotas <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >= ± <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F2 ALIGN=MIDDLE  ALT=\"x%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > pasa por el punto de coordenadas (5,2) \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >= ± <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29x ALIGN=MIDDLE  ALT=\"%281%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "intersection of the asymptotes is at origin: \r<BR>\n" );
document.write( "\n" );
document.write( "so, center is at: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=0+ ALIGN=MIDDLE  ALT=\"h=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=0 ALIGN=MIDDLE  ALT=\"k=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " asymptotesup-down <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >= ± <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Fb%29x ALIGN=MIDDLE  ALT=\"%28a%2Fb%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fb=1%2F2 ALIGN=MIDDLE  ALT=\"a%2Fb=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a=b ALIGN=MIDDLE  ALT=\"2a=b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "since passes through (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E2%2Fa%5E2-2%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"5%5E2%2Fa%5E2-2%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2Fa%5E2-4%2F%282a%29%5E2=1 ALIGN=MIDDLE  ALT=\"25%2Fa%5E2-4%2F%282a%29%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2Fa%5E2-4%2F4a%5E2=1 ALIGN=MIDDLE  ALT=\"25%2Fa%5E2-4%2F4a%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2Fa%5E2-1%2Fa%5E2=1 ALIGN=MIDDLE  ALT=\"25%2Fa%5E2-1%2Fa%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Fa%5E2=1 ALIGN=MIDDLE  ALT=\"24%2Fa%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=24 ALIGN=MIDDLE  ALT=\"a%5E2=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2a=2sqrt%2824%29 ALIGN=MIDDLE  ALT=\"b=2a=2sqrt%2824%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=4%2A24 ALIGN=MIDDLE  ALT=\"b%5E2=4%2A24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=96 ALIGN=MIDDLE  ALT=\"b%5E2=96\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2F24-x%5E2%2F96=1 ALIGN=MIDDLE  ALT=\"y%5E2%2F24-x%5E2%2F96=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );