document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=141988>Question 141988</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Describe the procedure used to write the standard equation of the ellipse defined by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9x%5E2%2B4y%5E2%2B18x-40y%2B73=0+ ALIGN=MIDDLE  ALT=\"+9x%5E2%2B4y%5E2%2B18x-40y%2B73=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #103398 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=103398\">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=9x%5E2%2B4y%5E2%2B18x-40y%2B73=0 ALIGN=MIDDLE  ALT=\"9x%5E2%2B4y%5E2%2B18x-40y%2B73=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=9x%5E2%2B18x%2B4y%5E2-40y%2B73=0 ALIGN=MIDDLE  ALT=\"9x%5E2%2B18x%2B4y%5E2-40y%2B73=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=9x%5E2%2B18x%2B4y%5E2-40y=-73 ALIGN=MIDDLE  ALT=\"9x%5E2%2B18x%2B4y%5E2-40y=-73\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=73 ALIGN=MIDDLE  ALT=\"73\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%28x%2B1%29%5E2-9%2B4y%5E2-40y=-73 ALIGN=MIDDLE  ALT=\"9%28x%2B1%29%5E2-9%2B4y%5E2-40y=-73\"   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=9%28x%2B1%29%5E2-9%2B4%28y-5%29%5E2-100=-73 ALIGN=MIDDLE  ALT=\"9%28x%2B1%29%5E2-9%2B4%28y-5%29%5E2-100=-73\"   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=9%28x%2B1%29%5E2%2B4%28y-5%29%5E2-109=-73 ALIGN=MIDDLE  ALT=\"9%28x%2B1%29%5E2%2B4%28y-5%29%5E2-109=-73\"   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=9%28x%2B1%29%5E2%2B4%28y-5%29%5E2=-73%2B109 ALIGN=MIDDLE  ALT=\"9%28x%2B1%29%5E2%2B4%28y-5%29%5E2=-73%2B109\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=109 ALIGN=MIDDLE  ALT=\"109\"   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=9%28x%2B1%29%5E2%2B4%28y-5%29%5E2=36 ALIGN=MIDDLE  ALT=\"9%28x%2B1%29%5E2%2B4%28y-5%29%5E2=36\"   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=%289%28x%2B1%29%5E2%2B4%28y-5%29%5E2%29%2F%2836%29=%2836%29%2F%2836%29 ALIGN=MIDDLE  ALT=\"%289%28x%2B1%29%5E2%2B4%28y-5%29%5E2%29%2F%2836%29=%2836%29%2F%2836%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >Now divide both sides by 36 to make the right side equal to 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%28x%2B1%29%5E2%29%2F%2836%29%2B%284%28y-5%29%5E2%29%2F%2836%29=1 ALIGN=MIDDLE  ALT=\"%289%28x%2B1%29%5E2%29%2F%2836%29%2B%284%28y-5%29%5E2%29%2F%2836%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%5E2%2F%284%29%2B%28y-5%29%5E2%2F%289%29=1 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%5E2%2F%284%29%2B%28y-5%29%5E2%2F%289%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So the equation is now in the standard form of an ellipse <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2F%28a%5E2%29%2B%28y-k%29%5E2%2F%28b%5E2%29=1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2F%28a%5E2%29%2B%28y-k%29%5E2%2F%28b%5E2%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-1 ALIGN=MIDDLE  ALT=\"h=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=5 ALIGN=MIDDLE  ALT=\"k=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3 ALIGN=MIDDLE  ALT=\"b=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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