document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=66246>Question 66246</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help sketch the graph and name the conic section with equation:<BR>\n" );
document.write( "4x^2-16x+9y^2+18y=0  So far I have factored out the 4 and 9. What comes next?Thank you  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #47972 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=47972\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm afraid the other solution that was posted for this problem is incorrect.  Anytime you have an equation of a conic section with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > with both having positive but unequal coefficients, it will be an ELLIPSE, NOT a PARABOLA. \r<BR>\n" );
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document.write( "If both coefficients are the same sign with equal coefficients, it will be a CIRCLE.  \r<BR>\n" );
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document.write( "If coefficients are of opposite sign, then it will be a HYPERBOLA.  \r<BR>\n" );
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document.write( "A PARABOLA results when there is an <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > but no <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > but no <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "This is the way it should be solved by completing the square:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-16x%2B9y%5E2%2B18y=0 ALIGN=MIDDLE  ALT=\"4x%5E2-16x%2B9y%5E2%2B18y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You must first factor out the coefficients of x^2 and y^2 like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x%5E2-4x%2B____%29%2B9%28y%5E2+%2B2y+%2B+_____%29=0 ALIGN=MIDDLE  ALT=\"4%28x%5E2-4x%2B____%29%2B9%28y%5E2+%2B2y+%2B+_____%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=4%28x%5E2-4x%2B4%29%2B9%28y%5E2+%2B2y+%2B+1%29=0%2B16%2B9 ALIGN=MIDDLE  ALT=\"4%28x%5E2-4x%2B4%29%2B9%28y%5E2+%2B2y+%2B+1%29=0%2B16%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x%5E2-4x%2B4%29%2B9%28y%5E2+%2B2y+%2B+1%29=25 ALIGN=MIDDLE  ALT=\"4%28x%5E2-4x%2B4%29%2B9%28y%5E2+%2B2y+%2B+1%29=25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This is an ellipse.  The standard form for an ellipse is in a form = 1, so divide both sides of the equation by 25 to set it equal to 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%28x-2%29%5E2%29%2F25+%2B%289%28y%2B+1%29%5E2%29%2F25=25%2F25 ALIGN=MIDDLE  ALT=\"%284%28x-2%29%5E2%29%2F25+%2B%289%28y%2B+1%29%5E2%29%2F25=25%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%28x-2%29%5E2%29%2F25+%2B%289%28y%2B+1%29%5E2%29%2F25=1 ALIGN=MIDDLE  ALT=\"%284%28x-2%29%5E2%29%2F25+%2B%289%28y%2B+1%29%5E2%29%2F25=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Finally invert the coefficients of 4 and 9 in order to write this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-2%29%5E2%29%2F%2825%2F4%29+%2B%28%28y%2B+1%29%5E2%29%2F%2825%2F9%29=1 ALIGN=MIDDLE  ALT=\"%28%28x-2%29%5E2%29%2F%2825%2F4%29+%2B%28%28y%2B+1%29%5E2%29%2F%2825%2F9%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "That would be standard form for an ellipse!  The center is at (2,-1), with the \"radius\" extending <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F2 ALIGN=MIDDLE  ALT=\"5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > units in the x direction, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F3 ALIGN=MIDDLE  ALT=\"5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > units in the y direction. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28300%2C300%2C-5%2C5%2C-5%2C5%2C+-1%2B%28sqrt%2825-4%28x-2%29%5E2%29%29%2F3%2C+-1-%28sqrt%2825-4%28x-2%29%5E2%29%29%2F3%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "R^2 at SCC\r<BR>\n" );
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