document.write( "Question 457430: What conic is described by the equation 4x^2 + 4y^2 - x + y = 0. Please show steps. Thank you. \n" ); document.write( "

Algebra.Com's Answer #313859 by Gogonati(855) $\"\"$ $\"About$

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To complete the squares we subtract 2/16=1/8 on the left side of equation.\r
\n" ); document.write( "\n" ); document.write( "= $\"%28%282x%29%5E2-x%2B1%2F16%29%2B%28%282y%29%5E2%2By%2B1%2F16%29=1%2F8\"$ => $\"%282x-1%2F4%29%5E2%2B%282y%2B1%2F4%29%5E2=1%2F8\"$ \r
\n" ); document.write( "\n" ); document.write( "Factoring the left side we get: $\"4%28x-1%2F8%29%5E2%2B4%28y%2B1%2F8%29%5E2=1%2F8\"$ , divide both sides \r
\n" ); document.write( "\n" ); document.write( "by 4 we get: $\"%28x-1%2F8%29%5E2%2B%28y%2B1%2F8%29%5E2=1%2F32\"$ The last equation represent a circle\r
\n" ); document.write( "\n" ); document.write( "centered at (1/8, -1/8) and radius $\"r=sqrt%282%29%2F8\"$ . \n" ); document.write( "

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