document.write( "Question 24796: I haven't taken algebra in 4 years I just need help refreshing. The problem says to find the center and the radius of the graph of the circle.
\n" ); document.write( "9x^2+9y^2-6y-17=0 \n" ); document.write( "

Algebra.Com's Answer #13237 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
First, you need to put your equation $\"9x%5E2+%2B+9y%5E2+-+6y+-+17+=+0\"$ into the standard form for a circle with centre at (h, k) and radius r. $\"%28x-h%29%5E2+%2B+%28y-k%29%5E2+=+r%5E2\"$
\n" ); document.write( "To accomplish this, you will need to \"complete the square\" in the y-terms. The x-term is already squared so it does not need to be changed. Here are the steps:
\n" ); document.write( "1) $\"9x%5E2+%2B+9y%5E2+-+6y+-+17+=+0\"$ Add 17 to both sides of the equation.
\n" ); document.write( "2) $\"9x%5E2+%2B+9y%5E2+-+6y+=+17\"$ Divide through by 9.
\n" ); document.write( "3) $\"%28x%5E2%29+%2B+%28y%5E2+-+%282%2F3%29y%29+=+17%2F9\"$ Complete the square in the y-terms by adding the square of half the y-coefficient (that's $\"%28%281%2F2%29%282%2F3%29%29%5E2+=+1%2F9\"$ ) to both sides of the equation.
\n" ); document.write( "4) $\"%28x%5E2%29+%2B+%28y%5E2+-+%282%2F3%29y+%2B+1%2F9%29+=+17+%2B+1%2F9\"$ Simplify and factor the y-group.
\n" ); document.write( "5) $\"%28x%5E2%29+%2B+%28y-1%2F3%29%5E2+=+154%2F9\"$ Rewrite the x-term as $\"%28x+-+0%29%5E2\"$
\n" ); document.write( "6) $\"%28x+-+0%29%5E2+%2B+%28y+-+1%2F3%29%5E2+=+154%2F9\"$ Compare this with the standard form:
\n" ); document.write( "7) $\"%28x+-+h%29%5E2+%2B+%28y+-+k%29%5E2+=+r%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( "You can see that the centre: (h, k) is (0, 1/3) and the radius, r, is $\"sqrt%28154%2F9%29+=+%281%2F3%29sqrt%28154%29\"$ \n" ); document.write( "

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