document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136333>Question 1136333</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the discriminant to determine whether the equation represents a parabola, hyperbola, or<BR>\n" );
document.write( "an ellipse. 4x^2  -  9xy  -  5y^2 + 15 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #754094 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=754094\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> recall:\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac%3C0 ALIGN=MIDDLE  ALT=\"b%5E2-4ac%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the equation represents an <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ellipse ALIGN=MIDDLE  ALT=\"ellipse\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "-A subordinate special case of this occurs when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=C+ ALIGN=MIDDLE  ALT=\"A=C+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+B=0 ALIGN=MIDDLE  ALT=\"+B=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the equation represents a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=circle ALIGN=MIDDLE  ALT=\"circle\"   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=b%5E2-4ac=0 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the equation represents a<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+parabola ALIGN=MIDDLE  ALT=\"+parabola\"   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=b%5E2-4ac+%3E0 ALIGN=MIDDLE  ALT=\"b%5E2-4ac+%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the equation represents a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=hyperbola ALIGN=MIDDLE  ALT=\"hyperbola\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "-A subordinate special case of this occurs, when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2BC=0 ALIGN=MIDDLE  ALT=\"A%2BC=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the equation represents a rectangular hyperbola.\r<BR>\n" );
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document.write( "you are given:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2+-+9xy+-+5y%5E2+%2B+15+=+0+ ALIGN=MIDDLE  ALT=\"4x%5E2+-+9xy+-+5y%5E2+%2B+15+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >...rearrange  the terms<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-+5y%5E2-+9xy%2B+4x%5E2%2B+15+=+0+ ALIGN=MIDDLE  ALT=\"+-+5y%5E2-+9xy%2B+4x%5E2%2B+15+=+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=-5 ALIGN=MIDDLE  ALT=\"a=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-9x ALIGN=MIDDLE  ALT=\"b=-9x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=4x%5E2%2B15 ALIGN=MIDDLE  ALT=\"c=4x%5E2%2B15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "discriminant is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-9x%29%5E2-4%2A%28-5%29%284x%5E2%2B15%29 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-9x%29%5E2-4%2A%28-5%29%284x%5E2%2B15%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=b%5E2-4ac=81x%5E2%2B20%284x%5E2%2B15%29 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=81x%5E2%2B20%284x%5E2%2B15%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=b%5E2-4ac=81x%5E2%2B80x%5E2%2B300 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=81x%5E2%2B80x%5E2%2B300\"   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%5E2-4ac=161x%5E2%2B300 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=161x%5E2%2B300\"   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%5E2-4ac+%3E+0 ALIGN=MIDDLE  ALT=\"b%5E2-4ac+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and your equation represents a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=hyperbola ALIGN=MIDDLE  ALT=\"hyperbola\"   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+-10%2C+10%2C+-10%2C+10%2C+-%281%2F10%29%28-sqrt%28161x%5E2%2B300%29-9x%29%2C%281%2F10%29+%28-sqrt%28161x%5E2%2B300%29-9x%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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