document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=129870>Question 129870</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sketch and identify the given conic\r<BR>\n" );
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document.write( "12 x^2 – 3y^2 – 18x - 3y – 10 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #94835 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=94835\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12+x%5E2+%96+3y%5E2+%96+18x+-+3y+%96+10+=+0 ALIGN=MIDDLE  ALT=\"12+x%5E2+%96+3y%5E2+%96+18x+-+3y+%96+10+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%5E2-18x-3y%5E2-3y-10=0 ALIGN=MIDDLE  ALT=\"12x%5E2-18x-3y%5E2-3y-10=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%5E2-18x-3y%5E2-3y=%2B10 ALIGN=MIDDLE  ALT=\"12x%5E2-18x-3y%5E2-3y=%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%28x-3%2F4%29%5E2-27%2F4-3y%5E2-3y=%2B10 ALIGN=MIDDLE  ALT=\"12%28x-3%2F4%29%5E2-27%2F4-3y%5E2-3y=%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Complete the square for the x terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%28x-3%2F4%29%5E2-27%2F4-3%28y%2B1%2F2%29%5E2%2B3%2F4=%2B10 ALIGN=MIDDLE  ALT=\"12%28x-3%2F4%29%5E2-27%2F4-3%28y%2B1%2F2%29%5E2%2B3%2F4=%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Complete the square for the y terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%28x-3%2F4%29%5E2-3%28y%2B1%2F2%29%5E2-24%2F4=%2B10 ALIGN=MIDDLE  ALT=\"12%28x-3%2F4%29%5E2-3%28y%2B1%2F2%29%5E2-24%2F4=%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%28x-3%2F4%29%5E2-3%28y%2B1%2F2%29%5E2-6=%2B10 ALIGN=MIDDLE  ALT=\"12%28x-3%2F4%29%5E2-3%28y%2B1%2F2%29%5E2-6=%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%28x-3%2F4%29%5E2-3%28y%2B1%2F2%29%5E2=%2B10%2B6 ALIGN=MIDDLE  ALT=\"12%28x-3%2F4%29%5E2-3%28y%2B1%2F2%29%5E2=%2B10%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%28x-3%2F4%29%5E2-3%28y%2B1%2F2%29%5E2=16 ALIGN=MIDDLE  ALT=\"12%28x-3%2F4%29%5E2-3%28y%2B1%2F2%29%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "-----------\r<BR>\n" );
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document.write( "Notice how the equation is now in the form <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;\" >. This means that this conic section is a hyperbola which opens up in the x direction.\r<BR>\n" );
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document.write( "So the conic section looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+sqrt%28%2864%2F4-12%28x-3%2F4%29%5E2%29%2F%28-3%29%29-1%2F2%2C-sqrt%28%2864%2F4-12%28x-3%2F4%29%5E2%29%2F%28-3%29%29-1%2F2%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%28x-3%2F4%29%5E2-3%28y%2B1%2F2%29%5E2=16 ALIGN=MIDDLE  ALT=\"12%28x-3%2F4%29%5E2-3%28y%2B1%2F2%29%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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