document.write( "Question 392026: The graph of the function x^2+y^2+20x-16y+80=0 is a circle. What are the coordinates of the center and the length of the radius?
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Algebra.Com's Answer #278235 by Earlsdon(6294) $\"\"$ $\"About$

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Find the center and length of radius of the circle:
\n" ); document.write( "Get the equation into standard form for a circle: $\"%28x-h%29%5E2%2B%28y-k%29%5E2+=+r%5E2\"$
\n" ); document.write( " $\"x%5E2%2By%5E2%2B20x-16y%2B80+=+0\"$ Group the terms:
\n" ); document.write( " $\"%28x%5E2%2B20x%29%2B%28y%5E2-16y%29%2B80+=+0\"$ Subtract 80 from both sides.
\n" ); document.write( " $\"%28x%5E2%2B20x%29%2B%28y%5E2-16y%29+=+-80\"$ } Complete the square in x and y.
\n" ); document.write( " $\"%28x%5E2%2B20x%2B100%29%2B%28y%5E2-16y%2B64%29+=+100%2B64-80\"$ Simplify.
\n" ); document.write( " $\"%28x%2B10%29%5E2+%2B+%28y-8%29%5E2+=+84\"$ Compare with standard form above:
\n" ); document.write( " $\"h+=+-10\"$ , $\"k+=+8\"$ , $\"r+=+sqrt%2884%29\"$
\n" ); document.write( "The coordinates of the center: (-10, 8)
\n" ); document.write( "Length of radius: $\"sqrt%2884%29\"$ = $\"9.165\"$ approx. \n" ); document.write( "

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