document.write( "Question 811442: x^2 + y^2 - 2x + 6y - 3 = 0 (find center and radius of the circle) \n" ); document.write( "
Algebra.Com's Answer #488739 by Edwin McCravy(20054) $\"\"$ $\"About$
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document.write( "We must get it in the standard form:\r\n" );
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document.write( "(x-h)² + (y-k)² = r²  where the center is (h,k) and the radius is r.\r\n" );
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document.write( " x² + 10x - 6y + 7 = 0\r\n" );
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document.write( "x² + y² - 2x + 6y - 3 = 0 \r\n" );
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document.write( "Get the x terms together and the y terms together\r\n" );
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document.write( "    x² - 2x + y² + 6y = 3\r\n" );
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document.write( "We must complete the square on each part, by adding\r\n" );
document.write( "a number after the x-terms and the y terms.  IOW we have\r\n" );
document.write( "blanks to fill in here:\r\n" );
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document.write( "x² - 2x + __ + y² + 6y + __ = 3 + __ + __\r\n" );
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document.write( "To fill in the first blank on the left and the first blank on the right\r\n" );
document.write( "side:\r\n" );
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document.write( "1. Multiply the coefficient of x which is -2 by  getting  -1\r\n" );
document.write( "2. Square this, getting (-1)² = +1\r\n" );
document.write( "3. Add this to both sides of the equation:\r\n" );
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document.write( "x² - 2x + 1 + y² + 6y + __ = 3 + 1 + __\r\n" );
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document.write( "To fill in the second blank on the left and the second blank on the right\r\n" );
document.write( "side:\r\n" );
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document.write( "1. Multiply the coefficient of y which is +6 by  getting  +3\r\n" );
document.write( "2. Square this, getting (+3)² = +9\r\n" );
document.write( "3. Add this to both sides of the equation:\r\n" );
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document.write( "x² - 2x + 1 + y² + 6y + 9 = 3 + 1 + 9 \r\n" );
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document.write( "The first three terms on the left side of \r\n" );
document.write( "the equation factor as x²-2x+1 = (x-1)(x-1) = (x-1)²\r\n" );
document.write( "The last three terms on the left side of \r\n" );
document.write( "the equation factor as y²+6y+9 = (y+3)(y+3) = (y+3)²\r\n" );
document.write( "We combine the numbers on the right side\r\n" );
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document.write( "(x-1)² + (y+3)² = 13\r\n" );
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document.write( "Compare that to the standard equation for a circle\r\n" );
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document.write( "(x-h)² + (y-k)² = r²  where the center is (h,k) and the radius is r.\r\n" );
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document.write( "We see by comparison that h=1, k=-3 and r = \r\n" );
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document.write( "So the center is (1,-3) and the radius is . \r\n" );
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document.write( "Edwin
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