document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=388048>Question 388048</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the radius of a circle defined by the equation: x^2+y^2+12x+6y+29=0. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #274364 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=274364\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(x\ -\ h\right)^2\ +\ \left(y\ -\ k\right)^2\ =\ r^2\">\r<BR>\n" );
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document.write( "is the equation of a circle centered at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(h,\,k\right)\"> with radius <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r\">\r<BR>\n" );
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document.write( "Take your standard form equation and complete the square on each of the variables.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ y^2\ +\ 12x\ +\ 6y\ +\ 29\ =\ 0\">\r<BR>\n" );
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document.write( "First move the constant to the RHS and group like variables:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ 12x\ +\ y^2\ +\ 6y\ =\ -\ 29\">\r<BR>\n" );
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document.write( "Take the coefficient on the first degree <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> term, divide by two, square the result, and add the squared result to both sides.  Do the same thing with the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> variable.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ 12x\ +\ 36\ +\ y^2\ +\ 6y\ +\ 9\ =\ -\ 29\ +\ 36\ +\ 9\">\r<BR>\n" );
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document.write( "Factor the two perfect square trinomials and collect terms in the RHS:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(x\ -\ (-6)\right)^2\ +\ \left(y\ -\ (-3)\right)^2\ =\ 16\">\r<BR>\n" );
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document.write( "From which you can determine the center by inspection and the radius by taking the positive square root of the RHS.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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