document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=83212>Question 83212</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the center and radius of the circle<BR>\n" );
document.write( "3x^2+y^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 #60042 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=60042\">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=3+%2A+x+%5E+2+%2B+y+%5E+2+-+6+%2A+x+%2B+4+%2A+y+-+4++++=0 ALIGN=MIDDLE  ALT=\"3+%2A+x+%5E+2+%2B+y+%5E+2+-+6+%2A+x+%2B+4+%2A+y+-+4++++=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given conic\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%2A+x+%5E+2+%2B+y+%5E+2+-+6+%2A+x+%2B+4+%2A+y+=+4+++ ALIGN=MIDDLE  ALT=\"3+%2A+x+%5E+2+%2B+y+%5E+2+-+6+%2A+x+%2B+4+%2A+y+=+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=%28+3+%2A+x+%5E+2+-+6+%2A+x+%29+%2B+%28+y+%5E+2+%2B+4+%2A+y+%29+=+4+++ ALIGN=MIDDLE  ALT=\"%28+3+%2A+x+%5E+2+-+6+%2A+x+%29+%2B+%28+y+%5E+2+%2B+4+%2A+y+%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+%28+x+%5E+2+-+2+%2A+x+%29+%2B+1+%28+y+%5E+2+%2B+4+%2A+y+%29+=+4+ ALIGN=MIDDLE  ALT=\"3+%28+x+%5E+2+-+2+%2A+x+%29+%2B+1+%28+y+%5E+2+%2B+4+%2A+y+%29+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor a 3 out of the first parenthesis<BR>\n" );
document.write( "and factor a 1 out of the second parenthesis.\r<BR>\n" );
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document.write( "Now we must complete the individual squares inside the parenthesis:\r<BR>\n" );
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document.write( " For instance to complete <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%28+x+%5E+2+-+2+%2A+x+%29+ ALIGN=MIDDLE  ALT=\"3+%28+x+%5E+2+-+2+%2A+x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, take half of -2 and square it (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%2F2%29%5E2=%28-1%29%5E2=1 ALIGN=MIDDLE  ALT=\"%28-2%2F2%29%5E2=%28-1%29%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 1. Now add 1 inside the parenthesis like this: \r<BR>\n" );
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document.write( "Since you really added <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A1 ALIGN=MIDDLE  ALT=\"3%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the entire left side, we must add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A1 ALIGN=MIDDLE  ALT=\"3%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the right side also. Now lets complete  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%28+y+%5E+2+%2B+4+%2A+y+%29 ALIGN=MIDDLE  ALT=\"1+%28+y+%5E+2+%2B+4+%2A+y+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In order to complete <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%28+y+%5E+2+%2B+4+%2A+y+%29 ALIGN=MIDDLE  ALT=\"1+%28+y+%5E+2+%2B+4+%2A+y+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, take half of 4 and square it (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F2%29%5E2=%282%29%5E2=4 ALIGN=MIDDLE  ALT=\"%284%2F2%29%5E2=%282%29%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 4. Now add 4 inside the parenthesis like this: \r<BR>\n" );
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document.write( "Since you really added <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2A4 ALIGN=MIDDLE  ALT=\"1%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the entire left side, we must add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2A4 ALIGN=MIDDLE  ALT=\"1%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the right side also.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%28+x+%5E+2+-+2+%2A+x+%2B+1+%29+%2B+1+%28+y+%5E+2+%2B+4+%2A+y+%2B+4+%29+=+-+4+%2B+3+%2B+4+%2A+1+++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Complete the individual squares by taking half of the 2nd coefficient and squaring it (remember to add to both sides).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%28+x+%5E+2+-+2+%2A+x+%2B+1+%29+%2B+1+%28+y+%5E+2+%2B+4+%2A+y+%2B+4+%29+=+1+1+ ALIGN=MIDDLE  ALT=\"3+%28+x+%5E+2+-+2+%2A+x+%2B+1+%29+%2B+1+%28+y+%5E+2+%2B+4+%2A+y+%2B+4+%29+=+1+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%28+x+-+1+%29+%5E+2+%2B+1+%28+y+%2B+2+%29+%5E+2+=+1+1+ ALIGN=MIDDLE  ALT=\"3+%28+x+-+1+%29+%5E+2+%2B+1+%28+y+%2B+2+%29+%5E+2+=+1+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the individual groups on the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28+3+%28+x+-+1+%29+%5E+2+%2B+1+%28+y+%2B+2+%29+%5E+2+%29+%2F+1+1+=+1+1+%2F+1+1+ ALIGN=MIDDLE  ALT=\"%28+3+%28+x+-+1+%29+%5E+2+%2B+1+%28+y+%2B+2+%29+%5E+2+%29+%2F+1+1+=+1+1+%2F+1+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 11\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%28+x+-+1+%29+%5E+2+%2F+1+1+%2B+1+%28+y+%2B+2+%29+%5E+2+%2F+1+1+=+1+ ALIGN=MIDDLE  ALT=\"3+%28+x+-+1+%29+%5E+2+%2F+1+1+%2B+1+%28+y+%2B+2+%29+%5E+2+%2F+1+1+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction 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( "So the equation is an ellipse where the center is (1,-2) \r<BR>\n" );
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document.write( "Here's the graph\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing+%28500%2C500%2C-10%2C+10%2C+-10%2C+10%2C%0D%0A+++ellipse%281%2C-2%2C2%2A1.91485421551268%2C2%2A3.3166247903554%29%2C%0D%0A+++circle%281%2C-2%2C0.08%29%2C%0D%0A+++circle%281%2C-2%2C0.05%29%2C%0D%0A+++graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C0%29%0D%0A+++%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%28+x+-+1+%29+%5E+2+%2F+1+1+%2B+1+%28+y+%2B+2+%29+%5E+2+%2F+1+1+=+1+ ALIGN=MIDDLE  ALT=\"3+%28+x+-+1+%29+%5E+2+%2F+1+1+%2B+1+%28+y+%2B+2+%29+%5E+2+%2F+1+1+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the center (1,-2) </SPAN>\n" );
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