document.write( "Question 16112: Given this equation find the radius and center of a circle. $\"x%5E2%2B6x%2By%5E2-5y=-1%2F4\"$ \n" ); document.write( "

Algebra.Com's Answer #7888 by Earlsdon(6294) $\"\"$ $\"About$

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You want to get your equation into the standard form for a circle with center at (h, k) and radius r. It will look like this:
\n" ); document.write( " $\"%28x+-+h%29%5E2+%2B+%28y+-+k%29%5E2+=+r%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( "To do this, you must:\r
\n" ); document.write( "\n" ); document.write( "1) Complete the square in the x-terms.
\n" ); document.write( "2) Complete the square in the y-terms.
\n" ); document.write( "3) Factor the resulting x-trinomial.
\n" ); document.write( "4) Factor the resulting y-trinomial.
\n" ); document.write( "5) Simplify, if necessary, into the standard form.\r
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2+%2B+6x%29+%2B+%28y%5E2+-+5y%29+=+-1%2F4\"$ Complete the squares by adding the square of half the coefficient of x/y to both sides.
\n" ); document.write( " $\"%28x%5E2+%2B+6x+%2B+9%29+%2B+%28y%5E2+-+5y+%2B+25%2F4%29+=+-1%2F4+%2B+9+%2B+25%2F4\"$ Factor the x and the y trinomials and simplify the right side of the equation.
\n" ); document.write( " $\"%28x+%2B+3%29%5E2+%2B+%28y+-+5%2F2%29%5E2+=+15\"$ Compare this with the standard form. $\"%28x-h%29%5E2+%2B+%28y-k%29%5E2+=+r%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( "The center of the circle is at (-3, 5/2) and the radius is $\"sqrt%2815%29\"$ \n" ); document.write( "

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