document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183543>Question 1183543</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of a hyperbola in the form y²/M - x²/N = 1, M, N> 0 if the center is at the origin, the length of the conjugate axis is 10, and the foci are sqrt(29) units from the center. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813921 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=813921\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2FM+-+x%5E2%2FN+=+1 ALIGN=MIDDLE  ALT=\"y%5E2%2FM+-+x%5E2%2FN+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M ALIGN=MIDDLE  ALT=\"M\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%3E+0 ALIGN=MIDDLE  ALT=\"N%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > if the center is at the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=origin ALIGN=MIDDLE  ALT=\"origin\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if given  the standard form <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;\" >, then foci have the form  (<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;\" >), and the transverse axis is the y-axis\r<BR>\n" );
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document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=sqrt%2829%29 ALIGN=MIDDLE  ALT=\"c=sqrt%2829%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " the foci are 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=sqrt%2829%29 ALIGN=MIDDLE  ALT=\"sqrt%2829%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<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=-sqrt%2829%29 ALIGN=MIDDLE  ALT=\"-sqrt%2829%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > )\r<BR>\n" );
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document.write( "in your case<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M=a%5E2 ALIGN=MIDDLE  ALT=\"M=a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=b%5E2 ALIGN=MIDDLE  ALT=\"N=b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the length of the conjugate axis is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a=10 ALIGN=MIDDLE  ALT=\"2a=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=5 ALIGN=MIDDLE  ALT=\"a=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=25 ALIGN=MIDDLE  ALT=\"a%5E2=25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"c%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=b%5E2=c%5E2-a%5E2 ALIGN=MIDDLE  ALT=\"b%5E2=c%5E2-a%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=29-25 ALIGN=MIDDLE  ALT=\"b%5E2=29-25\"   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=4 ALIGN=MIDDLE  ALT=\"b%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M=a%5E2=25 ALIGN=MIDDLE  ALT=\"M=a%5E2=25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=b%5E2=4 ALIGN=MIDDLE  ALT=\"N=b%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and your equation is:\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%2F4+=+1 ALIGN=MIDDLE  ALT=\"y%5E2%2F25+-+x%5E2%2F4+=+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=+graph%28+600%2C+600%2C+-15%2C+15%2C+-15%2C+25%2C++sqrt%28+25%28x%5E2%2F4+%2B1%29%29%2C+-sqrt%28+25%28x%5E2%2F4+%2B1%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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