document.write( "Question 226049: Please help me find the center (h,k) and radius r for the circle x^2+y^2+12x+10y+57=0 \n" ); document.write( "

Algebra.Com's Answer #168448 by LtAurora(115) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"x%5E2%2By%5E2%2B12x%2B10y%2B57=0\"$
\n" ); document.write( "Rewrite the equation:
\n" ); document.write( " $\"x%5E2%2B12x%2B___%2By%5E2%2B10y%2B___=-57%2B___%2B___\"$
\n" ); document.write( "We have to complete the square, so the blanks are filled in the $\"%28%281%2F2%29%2Ab%29%5E2\"$
\n" ); document.write( "For the x: $\"%28%281%2F2%29%2A12%29%5E2=36\"$
\n" ); document.write( "So, we fill in the blank like:
\n" ); document.write( " $\"x%5E2%2B12x%2B36%2By%5E2%2B10y%2B___=-57%2B36%2B___\"$
\n" ); document.write( "For the y: $\"%28%281%2F2%29%2A10%29%5E2=25\"$
\n" ); document.write( " $\"x%5E2%2B12x%2B36%2By%5E2%2B10y%2B25=-57%2B36%2B25\"$
\n" ); document.write( "The x term and the y term have to be factored, but that's easy now since they are completed squares. The x-term is simply $\"%281%2F2%29%2A12=6\"$ , and the y-term is $\"%281%2F2%29%2A10=5\"$ . Like this:
\n" ); document.write( " $\"%28x%2B6%29%5E2%2B%28y%2B5%29%5E2=4\"$
\n" ); document.write( "The center is the opposite of what's in the parentheses:
\n" ); document.write( "(-6,-5), with a radius of 2 (because $\"2%5E2=4\"$ ).
\n" ); document.write( "Good luck! \n" ); document.write( "

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