document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=126660>Question 126660</A>: <I><SPAN STYLE=\"word-break: break-all;\"> **Sorry if this appears twice, it doesn't seem to have worked the first time.\r<BR>\n" );
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document.write( "A hyperbola with the transverse axis on the line y=-5, length of transverse axis = 6, conjugate axis on the line x = 2, and length of conjugate axis = 6. \r<BR>\n" );
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document.write( "I need to use this information and put this hyperbola into an equation in the Ax2+By^2+cxy+Dx+Ey+F=0\r<BR>\n" );
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document.write( "So far, I know that the center is at (2,-5) and both a and b = 3. (at least I think)\r<BR>\n" );
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document.write( "I am really having problems putting it into the form that they ask. Help would be greatly appreciated!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #92811 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=92811\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> So far, so good.\r<BR>\n" );
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document.write( "The center is at (2,-5) because that is where the transverse and conjugate axes intersect, and both a and b = 3 because a is the length of the transverse axis divided by 2 and b is the length of the conjugate axis divided by 2.\r<BR>\n" );
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document.write( "Since the transverse axis is horizontal, this is an 'east-west' opening hyperbola.  The formula for such a hyperbola centered at (h,k) 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( "Substituting the coordinates of the center and the a and b values we get:\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%2F3%5E2-%28y-%28-5%29%29%5E2%2F3%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2F3%5E2-%28y-%28-5%29%29%5E2%2F3%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%2F9-%28y%2B5%29%5E2%2F9=1 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2F9-%28y%2B5%29%5E2%2F9=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-%28y%2B5%29%5E2=9 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2-%28y%2B5%29%5E2=9\"   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%5E2-4x%2B4-%28y%5E2%2B10y%2B25%29=9 ALIGN=MIDDLE  ALT=\"x%5E2-4x%2B4-%28y%5E2%2B10y%2B25%29=9\"   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%5E2-4x%2B4-%28y%5E2%2B10y%2B25%29=9 ALIGN=MIDDLE  ALT=\"x%5E2-4x%2B4-%28y%5E2%2B10y%2B25%29=9\"   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-y%5E2-4x-10y%2B4-25-9=0 ALIGN=MIDDLE  ALT=\"x%5E2-y%5E2-4x-10y%2B4-25-9=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=x%5E2-y%5E2-4x-10y-30=0 ALIGN=MIDDLE  ALT=\"x%5E2-y%5E2-4x-10y-30=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The correct form is actually:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ax%5E2+%2B+Bxy+%2B+Cy%5E2+%2B+Dx+%2B+Ey+%2B+F+=+0 ALIGN=MIDDLE  ALT=\"Ax%5E2+%2B+Bxy+%2B+Cy%5E2+%2B+Dx+%2B+Ey+%2B+F+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but it doesn't matter in this case because the coefficient on the xy term is 0.  You only get a non-zero coefficient on the xy term if the transverse and conjugate axes are other than parallel to the coordinate axes.<BR>\n" );
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