document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=24555>Question 24555</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the center of the circle x^2 + 4x + y^2 + 2y - 9 = 0? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #13070 by </B><A HREF=/tutors/aboutme.mpl?userid=kev82><B>kev82(151)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kev82><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=13070\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi,\r<BR>\n" );
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document.write( "The general equation of a circle as I'm sure you know is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-a%29%5E2%2B%28y-b%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%28x-a%29%5E2%2B%28y-b%29%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > where (a,b) is the centerpoint and r is the radius. We can make your equation look like this one by completing the square.\r<BR>\n" );
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document.write( "Firstly we're looking for the value of a such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-a%29%5E2=x%5E2%2B4x ALIGN=MIDDLE  ALT=\"%28x-a%29%5E2=x%5E2%2B4x\"   DISABLED_style= \"max-width:90%; height:auto;\" > You can either just guess that <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;\" > or expand and compare coefficients. But <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-%28-2%29%29%5E2=x%5E2%2B4x%2B4 ALIGN=MIDDLE  ALT=\"%28x-%28-2%29%29%5E2=x%5E2%2B4x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x=%28x%2B2%29%5E2-4 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x=%28x%2B2%29%5E2-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Doing the same for y, we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2B2y=%28y%2B1%29%5E2-1 ALIGN=MIDDLE  ALT=\"y%5E2%2B2y=%28y%2B1%29%5E2-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Finally substituting into the equation we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%5E2+%2B+%28y%2B1%29%5E2+-4+-1+-9=0 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2+%2B+%28y%2B1%29%5E2+-4+-1+-9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, in the standard form for a circle we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%5E2+%2B+%28y%2B1%29%5E2+=14 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2+%2B+%28y%2B1%29%5E2+=14\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So we can read off from this that the circle is centered at (-2,-1) with a radius of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2814%29 ALIGN=MIDDLE  ALT=\"sqrt%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Hope that helps, <BR>\n" );
document.write( "Kev </SPAN>\n" );
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