document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=83203>Question 83203</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the center and radius of the circle<BR>\n" );
document.write( "3x^2+4y^2-6x+4y-4=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #59735 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=59735\">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=3x%5E2%2B4y%5E2-6x%2B4y-4=0 ALIGN=MIDDLE  ALT=\"3x%5E2%2B4y%5E2-6x%2B4y-4=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=3x%5E2%2B4y%5E2-6x%2B4y=4 ALIGN=MIDDLE  ALT=\"3x%5E2%2B4y%5E2-6x%2B4y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > add 4 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E2-6x%29%2B%284y%5E2%2B4y%29=4 ALIGN=MIDDLE  ALT=\"%283x%5E2-6x%29%2B%284y%5E2%2B4y%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x%5E2-2x%29%2B4%28y%5E2%2By%29=4 ALIGN=MIDDLE  ALT=\"3%28x%5E2-2x%29%2B4%28y%5E2%2By%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x%5E2-2x%2B1%29%2B4%28y%5E2%2By%2B1%2F4%29=4%2B3%2B1 ALIGN=MIDDLE  ALT=\"3%28x%5E2-2x%2B1%29%2B4%28y%5E2%2By%2B1%2F4%29=4%2B3%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Complete the squares of each parenthesis (remember to add to both sides)\r<BR>\n" );
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document.write( "Since we completed the squares, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x-1%29%5E2%2B4%28y%2B1%2F2%29%5E2=8 ALIGN=MIDDLE  ALT=\"3%28x-1%29%5E2%2B4%28y%2B1%2F2%29%5E2=8\"   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=%283%28x-1%29%5E2%2B4%28y%2B1%2F2%29%5E2%29%2F8=8%2F8 ALIGN=MIDDLE  ALT=\"%283%28x-1%29%5E2%2B4%28y%2B1%2F2%29%5E2%29%2F8=8%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now divide both sides by 4 to get the equation into standard form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%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=3%28x-1%29%5E2%2F8%2B%28y%2B1%2F2%29%5E2%2F2=1 ALIGN=MIDDLE  ALT=\"3%28x-1%29%5E2%2F8%2B%28y%2B1%2F2%29%5E2%2F2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the equation is actually an ellipse (check your problem again) where the radii are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%288%2F3%29 ALIGN=MIDDLE  ALT=\"sqrt%288%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the center is (1,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) </SPAN>\n" );
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