document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=139738>Question 139738</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me with this problem. It is from a mathe work sheet. Thnak you.\r<BR>\n" );
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document.write( "Find the center and the radius of the circle.\r<BR>\n" );
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document.write( "4.) x2 + 12x + 36 + (y-4)2 = 49 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #101849 by </B><A HREF=/tutors/aboutme.mpl?userid=JSmall><B>JSmall(7)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=JSmall><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=101849\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The most useful form of the equation of a circle is:<BR>\n" );
document.write( "  ( x - h )^2 + ( y - k )^2 = r^2<BR>\n" );
document.write( "When the equation of a circle is written this way, the center of the circle can be easily read: (h, k). And the radius, r, can also be read easily.\r<BR>\n" );
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document.write( "So to solve your problem we need to use Algebra to change your original equation:<BR>\n" );
document.write( "  x^2 + 12x + 36 + ( y - 4 )^2 = 49<BR>\n" );
document.write( "to one that looks like:<BR>\n" );
document.write( "  ( x - h )^2 + ( y - k )^2 = r^2\r<BR>\n" );
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document.write( "As I hope you can see, your original equation already has \"y\" in the proper form. All we need to do is change <BR>\n" );
document.write( "  x^2 + 12x + 36<BR>\n" );
document.write( "to something like<BR>\n" );
document.write( "  ( x - h )^2<BR>\n" );
document.write( "and change whatever number is on the right to something like<BR>\n" );
document.write( "  r^2\r<BR>\n" );
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document.write( "To change <BR>\n" );
document.write( "  x^2 + 12x + 36<BR>\n" );
document.write( "to something like<BR>\n" );
document.write( "  ( x - h )^2<BR>\n" );
document.write( "we do something called \"completing the square\".\r<BR>\n" );
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document.write( "For<BR>\n" );
document.write( "  x^2 + 12x + 36<BR>\n" );
document.write( "completing the square happens to be very easy.<BR>\n" );
document.write( "  x^2 + 12x + 36<BR>\n" );
document.write( "is equal to <BR>\n" );
document.write( "  ( x + 6 )^2<BR>\n" );
document.write( "(If this is not obvious, multiply ( x + 6 ) ( x + 6 )  [Most people use \"FOIL\" for this.] and see that<BR>\n" );
document.write( "   x^2 + 12x + 36 = ( x + 6 )^2\r<BR>\n" );
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document.write( "Now ( x + 6 )^2 is not quite in the form ( x - h )^2. We need to rewrite it as a subtraction: ( x + 6 )^2 = ( x - (-6))^2\r<BR>\n" );
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document.write( "The only thing remaining is to rewrite the 49 on the right side as something squared. Since 49 = 7^2 this is pretty simple.\r<BR>\n" );
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document.write( "So our final version of the equation is<BR>\n" );
document.write( "  ( x - (-6))^2 + ( y - 4 )^2 = 7^2\r<BR>\n" );
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document.write( "The center of the circle is (-6, 4) and the radius is 7.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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