document.write( "Question 140633This question is from textbook algebra 2
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Algebra.Com's Answer #102358 by Edwin McCravy(20056)\"\" \"About 
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document.write( "        x² + 12x + y² + 12y + 36 = 0\r\n" );
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document.write( "That's the equation of a circle because it \r\n" );
document.write( "contains both an x² and y² with the same coefficient\r\n" );
document.write( "when on the same side of the equation.\r\n" );
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document.write( "We must get it in standard form, which is\r\n" );
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document.write( "             (x - h)² + (y - k)² = r²\r\n" );
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document.write( "where the center is (h,k) and the radius is r. \r\n" );
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document.write( "You must memorize that standard form and those facts\r\n" );
document.write( "about h, k, and r.\r\n" );
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document.write( "Starting with \r\n" );
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document.write( "        x² + 12x + y² + 12y + 36 = 0\r\n" );
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document.write( "Get the constant term 36 off the left side\r\n" );
document.write( "Subtract 36 from both sides of the equation:\r\n" );
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document.write( "             x² + 12x + y² + 12y = -36 \r\n" );
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document.write( "Complete the square on the x's:\r\n" );
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document.write( "Take half of 12, the coefficient of x,\r\n" );
document.write( "which is 6.  Then square 6 and get 36.\r\n" );
document.write( "Now add 36 to both sides:\r\n" );
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document.write( "        x² + 12x + 36 + y² + 12y = -36 + 36 \r\n" );
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document.write( "Complete the square on the y's:\r\n" );
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document.write( "Take half of 12, the coefficient of y,\r\n" );
document.write( "which is 6.  Then square 6 and get 36.\r\n" );
document.write( "Now add 36 to both sides:\r\n" );
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document.write( "   x² + 12x + 36 + y² + 12y + 36 = -36 + 36 + 36\r\n" );
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document.write( "Factor the first three terms as (x + 6)(x + 6) and as (x + 6)²\r\n" );
document.write( "and combine the terms on the right\r\n" );
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document.write( "        (x + 6)² + y² + 12y + 36 = 36\r\n" );
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document.write( "Factor the next three terms as (y + 6)(y + 6) and as (y + 6)²\r\n" );
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document.write( "        (x + 6)² + (y + 6)² = 36 \r\n" );
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document.write( "Now we compare with the standard form:\r\n" );
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document.write( "        (x - h)² + (y - k)² = r²\r\n" );
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document.write( "And see that -h = +6 or h = -6, -k = 6, so k = -6, and r² = 36\r\n" );
document.write( "so r = 6.\r\n" );
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document.write( "So the equation is that of a circle with radius 6 and \r\n" );
document.write( "center (-6,-6)\r\n" );
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document.write( "Edwin
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