document.write( "Question 833445: FIND THE EQATION OF CIRCLE CONCENTRIC WITH THE CIRCLE X2+Y2-2X-6Y+4=0 AND HAVING RADIUS 7? \n" ); document.write( "
Algebra.Com's Answer #502580 by Edwin McCravy(20055)\"\" \"About 
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document.write( "FIND THE EQATION OF CIRCLE CONCENTRIC WITH THE CIRCLE X2+Y2-2X-6Y+4=0 AND HAVING RADIUS 7?\r\n" );
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document.write( "First we write the equation of the circle\r\n" );
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document.write( "x² + y² - 2x - 6y + 4 = 0\r\n" );
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document.write( "In the form \r\n" );
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document.write( "(x - h)² + (y-k)² = r²\r\n" );
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document.write( "x² + y² - 2x - 6y + 4 = 0\r\n" );
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document.write( "Rearrange so that the x terms and the y terms are together \r\n" );
document.write( "and the constant term on the right. \r\n" );
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document.write( "x² - 2x + y² - 6y = -4 \r\n" );
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document.write( "Place the x terms and the y terms in parentheses\r\n" );
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document.write( "(x² - 2x) + (y² - 6y) = -4\r\n" );
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document.write( "Complete the square in both parentheses by the rule\r\n" );
document.write( "1. Multiply the coefficient of the second term in each parentheses by 1/2\r\n" );
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document.write( "(-2)(1/2) = -1\r\n" );
document.write( "(-6)(1/2) = -3\r\n" );
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document.write( "2. Square the results:\r\n" );
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document.write( "(-1)² = +1\r\n" );
document.write( "(-3)² = +9\r\n" );
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document.write( "3. Add at the end of each parentheses and to the opposite side.\r\n" );
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document.write( "(x² - 2x + 1) + (y² - 6y + 9) = -4 + 1 + 9\r\n" );
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document.write( "Factor each parenthetical expression as the square of a binomial on the left\r\n" );
document.write( "and combine the terms on the right:\r\n" );
document.write( "(x² - 2x + 1) = (x - 1)(x - 1) = (x - 1)²\r\n" );
document.write( "(y² - 6y + 9) = (y - 3)(y - 3) = (x - 3)²\r\n" );
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document.write( "(x - 1)² + (y - 3)² = 6\r\n" );
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document.write( "Compare this to \r\n" );
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document.write( "(x - h)² + (y - k)² = r²\r\n" );
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document.write( "h=1, k = 3, r² = 6, so r = √6\r\n" );
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document.write( "The center = (h,k) = (1, 3) and the radius is √6\r\n" );
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document.write( "The desired circle has the same center (1,3) but a different radius,\r\n" );
document.write( "7.\r\n" );
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document.write( "So the left side of the equation of the circle you wish to find\r\n" );
document.write( "will be the same as the left side of the circle you were given,\r\n" );
document.write( "but the right side will be r² = 7² or r = 49 instead of 6.\r\n" );
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document.write( "Answer:  (x - 1)² + (y - 3)² = 49\r\n" );
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document.write( "The green circle is the circle you were given, and the red circle\r\n" );
document.write( "is the one you were asked to find.\r\n" );
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document.write( "Edwin
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