document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=928231>Question 928231</A>: <I><SPAN STYLE=\"word-break: break-all;\">  find equation of hyperbola where foci is (9,0) and hyperbola passes through (12,3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #563539 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=563539\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find equation of hyperbola where foci is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   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;\" >) and hyperbola passes through (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "The general formula of a hyperbola is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2F+a%5E2+-+y%5E2+%2F+b%5E2=+1 ALIGN=MIDDLE  ALT=\"x%5E2+%2F+a%5E2+-+y%5E2+%2F+b%5E2=+1\"   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=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is a point on the hyperbola, we have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%5E2+%2F+a%5E2+-+3%5E2+%2F+b%5E2+=+1 ALIGN=MIDDLE  ALT=\"12%5E2+%2F+a%5E2+-+3%5E2+%2F+b%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=144+%2F+a%5E2+-+9+%2F+b%5E2+=+1 ALIGN=MIDDLE  ALT=\"144+%2F+a%5E2+-+9+%2F+b%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >........eq.(1)\r<BR>\n" );
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document.write( "Since the foci is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   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;\" >), we have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+b%5E2+=+9%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2+=+9%5E2\"   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+=+81+-+a%5E2 ALIGN=MIDDLE  ALT=\"b%5E2+=+81+-+a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.(2)\r<BR>\n" );
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document.write( "Substituting (2) into (1), we have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144+%2F+a%5E2+-+9+%2F+%2881-a%5E2%29+=+1 ALIGN=MIDDLE  ALT=\"144+%2F+a%5E2+-+9+%2F+%2881-a%5E2%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ....common denominator is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2881-a%5E2%29 ALIGN=MIDDLE  ALT=\"a%5E2%2881-a%5E2%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=%28144%2881-a%5E2%29-9a%5E2%29%2F%28a%5E2%2881-a%5E2%29%29=1 ALIGN=MIDDLE  ALT=\"%28144%2881-a%5E2%29-9a%5E2%29%2F%28a%5E2%2881-a%5E2%29%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=%28144%2881-a%5E2%29-9a%5E2%29=1%28a%5E2%2881-a%5E2%29%29 ALIGN=MIDDLE  ALT=\"%28144%2881-a%5E2%29-9a%5E2%29=1%28a%5E2%2881-a%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=11664-144a%5E2-9a%5E2=81a%5E2-a%5E4 ALIGN=MIDDLE  ALT=\"11664-144a%5E2-9a%5E2=81a%5E2-a%5E4\"   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=0=144a%5E2%2B81a%5E2%2B9a%5E2-a%5E4-11664 ALIGN=MIDDLE  ALT=\"0=144a%5E2%2B81a%5E2%2B9a%5E2-a%5E4-11664\"   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=0=234a%5E2-a%5E4-11664 ALIGN=MIDDLE  ALT=\"0=234a%5E2-a%5E4-11664\"   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%5E4-234a%5E2%2B11664=0 ALIGN=MIDDLE  ALT=\"a%5E4-234a%5E2%2B11664=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >....write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-234a%5E2 ALIGN=MIDDLE  ALT=\"-234a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-162a%5E2-72x%5E2 ALIGN=MIDDLE  ALT=\"-162a%5E2-72x%5E2\"   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%5E4-162a%5E2-72x%5E2%2B11664=0 ALIGN=MIDDLE  ALT=\"a%5E4-162a%5E2-72x%5E2%2B11664=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=%28a%5E4-162a%5E2%29-%2872x%5E2%2B11664%29=0 ALIGN=MIDDLE  ALT=\"%28a%5E4-162a%5E2%29-%2872x%5E2%2B11664%29=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=a%5E2%28a%5E2-162%29-72%28x%5E2%2B162%29=0 ALIGN=MIDDLE  ALT=\"a%5E2%28a%5E2-162%29-72%28x%5E2%2B162%29=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=%28a%5E2-162%29%28a%5E2-72%29+=+0 ALIGN=MIDDLE  ALT=\"%28a%5E2-162%29%28a%5E2-72%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E2-162%29+=+0 ALIGN=MIDDLE  ALT=\"%28a%5E2-162%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+=+162 ALIGN=MIDDLE  ALT=\"a%5E2+=+162\"   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=%28a%5E2-72%29+=+0 ALIGN=MIDDLE  ALT=\"%28a%5E2-72%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+=+72 ALIGN=MIDDLE  ALT=\"a%5E2+=+72\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Suppose <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+=+162 ALIGN=MIDDLE  ALT=\"a%5E2+=+162\"   DISABLED_style= \"max-width:90%; height:auto;\" >, from (2), we have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+=+81+-+162+=+-81 ALIGN=MIDDLE  ALT=\"b%5E2+=+81+-+162+=+-81\"   DISABLED_style= \"max-width:90%; height:auto;\" >=>rejected, since a square cannot be negative \r<BR>\n" );
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document.write( "Suppose <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+=+72 ALIGN=MIDDLE  ALT=\"a%5E2+=+72\"   DISABLED_style= \"max-width:90%; height:auto;\" >, from (2), we have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+=+81-72+=+9 ALIGN=MIDDLE  ALT=\"b%5E2+=+81-72+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> this solution is accepted\r<BR>\n" );
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document.write( "Thus, we have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F72+-y%5E2%2F9+=+1 ALIGN=MIDDLE  ALT=\"x%5E2%2F72+-y%5E2%2F9+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "foci is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   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;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9 ALIGN=MIDDLE  ALT=\"-9\"   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;\" >)\r<BR>\n" );
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document.write( "hyperbola passes through (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   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=drawing%28+600%2C+600%2C+-25%2C+25%2C+-25%2C25%2Clocate%2812%2C3%2Cp%2812%2C3%29%29%2C+circle%2812%2C3%2C.3%29%2Ccircle%28-9%2C0%2C.3%29%2Ccircle%289%2C0%2C.3%29%2Cgraph%28+600%2C+600%2C+-25%2C+25%2C+-25%2C+25%2Csqrt%289x%5E2%2F72-9%29%2C-sqrt%289x%5E2%2F72-9%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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