document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=138452>Question 138452</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the center and radius by completing the square!<BR>\n" );
document.write( "x^2+y^2-4ax-6ay+4a=0<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #101100 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=101100\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I did this problem on paper before I started writing the response, and I would be willing to bet that you forgot a ^2 on the 4a term because the radius comes out so horribly ugly otherwise.  I'll show you both ways, just in case.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2-4ax-6ay%2B4a=0 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2-4ax-6ay%2B4a=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 1:  Put the constant term on the left.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2-4ax-6ay=-4a ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2-4ax-6ay=-4a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 2:  Put the x-terms together and the y-terms together.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4ax%2By%5E2-6ay=-4a ALIGN=MIDDLE  ALT=\"x%5E2-4ax%2By%5E2-6ay=-4a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 3:  Divide the coefficient on the 1st degree x-term by 2 and then square the result.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284a%2F2%29%5E2=%282a%29%5E2=4a%5E2 ALIGN=MIDDLE  ALT=\"%284a%2F2%29%5E2=%282a%29%5E2=4a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Add the result to both sides of the equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4ax%2B4a%5E2%2By%5E2-6ay=-4a%2B4a%5E2 ALIGN=MIDDLE  ALT=\"x%5E2-4ax%2B4a%5E2%2By%5E2-6ay=-4a%2B4a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 4: Repeat step 3 for the y terms:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286a%2F2%29%5E2=%283a%29%5E2=9a%5E2 ALIGN=MIDDLE  ALT=\"%286a%2F2%29%5E2=%283a%29%5E2=9a%5E2\"   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=x%5E2-4ax%2B4a%5E2%2By%5E2-6ay%2B9a%5E2=-4a%2B4a%5E2%2B9a%5E2 ALIGN=MIDDLE  ALT=\"x%5E2-4ax%2B4a%5E2%2By%5E2-6ay%2B9a%5E2=-4a%2B4a%5E2%2B9a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 5: Collect terms on the right, and factor the two perfect squares on the left\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2a%29%5E2%2B%28y-3a%29%5E2=13a%5E2-4a ALIGN=MIDDLE  ALT=\"%28x-2a%29%5E2%2B%28y-3a%29%5E2=13a%5E2-4a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The equation of a circle with center at (h,k) and radius r is:\r<BR>\n" );
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document.write( "So the center of your circle is (2a,3a) and the radius is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2813a%5E2-4a%29 ALIGN=MIDDLE  ALT=\"sqrt%2813a%5E2-4a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <big><b>UGH!</big></b>\r<BR>\n" );
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document.write( "If the original equation is really <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2-4ax-6ay%2B4a%5E2=0 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2-4ax-6ay%2B4a%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the center comes out the same, but the radius is a nice neat <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289a%5E2%29=3a ALIGN=MIDDLE  ALT=\"sqrt%289a%5E2%29=3a\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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