document.write( "Question 24555: what is the center of the circle x^2 + 4x + y^2 + 2y - 9 = 0? \n" ); document.write( "

Algebra.Com's Answer #13071 by askmemath(368) $\"\"$ $\"About$

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Equation of a circle is given by $\"%28x-a%29%5E2+%2B+%28y-b%29%5E2+=+r%5E2\"$ where (a,b) is the center of the circle and r is the radius.\r
\n" ); document.write( "\n" ); document.write( "Therefore we need to write x^2 + 4x + y^2 + 2y - 9 = 0 in form above.
\n" ); document.write( "Since I have $\"x%5E2+%2B+4x\"$ all i need to do is add 4 and i can re-write it as $\"%28x%2B2%29%5E2\"$ However if I am adding 4 then I also need to subtract 4 from the equation
\n" ); document.write( "So i get $\"%28x%2B2%29%5E2+%2B+y%5E2+%2B2y+-+9+-+4+=+0\"$ \r
\n" ); document.write( "\n" ); document.write( "Similarly for $\"y%5E2+%2B2y+\"$ I can add 1 and re-write as $\"%28y%2B1%29%5E2\"$ and similarly subtract 1\r
\n" ); document.write( "\n" ); document.write( " $\"%28x%2B2%29%5E2+%2B+%28y%2B1%29%5E2+-9-4-1+=+0\"$
\n" ); document.write( "Adding 14 on both sides
\n" ); document.write( " $\"%28x%2B2%29%5E2+%2B+%28y%2B1%29%5E2=+14\"$ \r
\n" ); document.write( "\n" ); document.write( "so center of circle becomes (-2,-1) and radius becomes $\"sqrt%2814%29\"$ \n" ); document.write( "

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