document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1180953>Question 1180953</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation in standard form of the hyperbola whose foci are F1(−4√2, 0) and F2(4√2, 0), such that for any point on it, the absolute value of the difference of its distances from the foci is 8. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #810944 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=810944\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have the distance between the foci is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8sqrt%282%29+=+2c ALIGN=MIDDLE  ALT=\"8sqrt%282%29+=+2c\"   DISABLED_style= \"max-width:90%; height:auto;\" > -> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=4sqrt%282%29 ALIGN=MIDDLE  ALT=\"c+=4sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "A property of hyperbolas is that the absolute value of the difference of the distances from the foci is equal to the length of the transverse axis: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8+=+2a ALIGN=MIDDLE  ALT=\"8+=+2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > -> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+4 ALIGN=MIDDLE  ALT=\"a+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Another property is that \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+=+c%5E2+ ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2+=+c%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "from which you can find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > (half the conjugate axis), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+4 ALIGN=MIDDLE  ALT=\"b+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Since the foci are on a horizontal line, your hyperbola is oriented <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=horizontally ALIGN=MIDDLE  ALT=\"horizontally\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=center ALIGN=MIDDLE  ALT=\"center\"   DISABLED_style= \"max-width:90%; height:auto;\" > halfway between the foci, in this case 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( "So the equation is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Fa%5E2+-+y%5E2%2Fb%5E2+=+1+ ALIGN=MIDDLE  ALT=\"x%5E2%2Fa%5E2+-+y%5E2%2Fb%5E2+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+b+=+4 ALIGN=MIDDLE  ALT=\"a+=+b+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > in this case. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F4%5E2+-+y%5E2%2F4%5E2+=+1+ ALIGN=MIDDLE  ALT=\"x%5E2%2F4%5E2+-+y%5E2%2F4%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%2F16+-+y%5E2%2F16+=+1+ ALIGN=MIDDLE  ALT=\"x%5E2%2F16+-+y%5E2%2F16+=+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=drawing+%28+600%2C+600%2C+-15%2C+15%2C+-15%2C+15%2C%0D%0Acircle%284sqrt%282%29%2C+0%2C.15%29%2Clocate%284sqrt%282%29%2C+0.7%2CF%29%2C%0D%0Acircle%28-4sqrt%282%29%2C+0%2C.15%29%2Clocate%28-4sqrt%282%29%2C+0.7%2CF%29%2C%0D%0Agraph%28+600%2C+600%2C+-15%2C+15%2C+-15%2C+15%2C-sqrt%28x%5E2+-+16%29%2Csqrt%28x%5E2+-+16%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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