document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197350>Question 1197350</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation (hyperbola)<BR>\n" );
document.write( "asymptotes y  -  3 = √13/6 (x-2) and focus at (9, 3)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #830607 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=830607\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "the equation (hyperbola)  is:\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%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;\" >\r<BR>\n" );
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document.write( "Find the equation (hyperbola) if the\r<BR>\n" );
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document.write( "asymptotes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+-+3+=+%28sqrt%2813%29%2F6%29+%28x-2%29+ ALIGN=MIDDLE  ALT=\"y+-+3+=+%28sqrt%2813%29%2F6%29+%28x-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y++=+%28sqrt%2813%29%2F6%29+%28x-2%29+%2B3 ALIGN=MIDDLE  ALT=\"y++=+%28sqrt%2813%29%2F6%29+%28x-2%29+%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and focus at (<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=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "The first asymptote is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=++-+%28b%2Fa+%29%28x-h%29%2Bk ALIGN=MIDDLE  ALT=\"y=++-+%28b%2Fa+%29%28x-h%29%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "compare to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y++=+%28sqrt%2813%29%2F6%29+%28x-2%29+%2B3+ ALIGN=MIDDLE  ALT=\"y++=+%28sqrt%2813%29%2F6%29+%28x-2%29+%2B3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and you see that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=3 ALIGN=MIDDLE  ALT=\"k=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=-%28b%2Fa+%29=+%28sqrt%2813%29%2F6%29 ALIGN=MIDDLE  ALT=\"-%28b%2Fa+%29=+%28sqrt%2813%29%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  =><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;\" > and<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=+sqrt%2813%29 ALIGN=MIDDLE  ALT=\"b=+sqrt%2813%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "take into account different properties of a hyperbola:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28h-9%29%5E2=a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"%28h-9%29%5E2=a%5E2%2Bb%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=%28h-9%29%5E2=49 ALIGN=MIDDLE  ALT=\"%28h-9%29%5E2=49\"   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=%28h-9%29=7 ALIGN=MIDDLE  ALT=\"%28h-9%29=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28h-9%29=-7 ALIGN=MIDDLE  ALT=\"+%28h-9%29=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28h-9%29=7 ALIGN=MIDDLE  ALT=\"%28h-9%29=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=16 ALIGN=MIDDLE  ALT=\"h=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28h-9%29=-7 ALIGN=MIDDLE  ALT=\"%28h-9%29=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=2+ ALIGN=MIDDLE  ALT=\"h=2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "substitute in equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=2 ALIGN=MIDDLE  ALT=\"h=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=3 ALIGN=MIDDLE  ALT=\"k=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=sqrt%2813%29 ALIGN=MIDDLE  ALT=\"b=sqrt%2813%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=%28x-2%29%5E2%2F6%5E2-%28y-3%29%5E2%2F%28sqrt%2813%29%29%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2F6%5E2-%28y-3%29%5E2%2F%28sqrt%2813%29%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=%28x-2%29%5E2%2F36-%28y-3%29%5E2%2F13=1 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2F36-%28y-3%29%5E2%2F13=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2%2F36-%28y-3%29%5E2%2F13=1 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2F36-%28y-3%29%5E2%2F13=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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