document.write( "Question 201163: find the radius of a circle:
\n" ); document.write( "x^2+y^2-12x+8y+43=0 \n" ); document.write( "

Algebra.Com's Answer #151381 by Earlsdon(6294) $\"\"$ $\"About$

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Find the radius of the circle:
\n" ); document.write( " $\"x%5E2%2By%5E2-12x%2B8y%2B43+=+0\"$
\n" ); document.write( "To do this, you need to change the given equation into the general form for a circle with center at (h, k) and radius, r,: $\"%28x-h%29%5E2%2B%28y-k%29%5E2+=+r%5E2\"$ .
\n" ); document.write( "You can do this by using the method of \"completing the square\".
\n" ); document.write( "First, group the terms of the given equation as shown:
\n" ); document.write( " $\"%28x%5E2-12x%29%2B%28y%5E2%2B8y%29%2B43+=+0\"$ Next, subtract 43 from both sides of the equation.
\n" ); document.write( " $\"%28x%5E2-12x%29%2B%28y%5E2%2B8y%29+=+-43\"$ Now complete the square in the x-group and in the y-group by adding the square of half the x-coefficient and the square of half the y-coefficient to both sides of the equation.
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Now factor the x-trinomial and the y-trinomial and simplify the right side of the equation.
\n" ); document.write( " $\"%28x-6%29%5E2%2B%28y%2B4%29%5E2+=+9\"$ Compare this result with the standard form given above:
\n" ); document.write( " $\"%28x-h%29%5E2%2B%28y-k%29%5E2+=+r%5E2\"$
\n" ); document.write( "You can see that the radius squared is $\"r%5E2+=+9\"$ so the radius must be $\"highlight%28r+=+3%29\"$ and, incidentally, you now have the center of the circle, (h, k) and it's ( $\"6\"$ , $\"-4\"$ ) \n" ); document.write( "

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