document.write( "Question 643602: i am trying to find the center and radius of X2+Y2+4X-8Y+13=0
\n" ); document.write( "So far i think its (x+2)^2+(y-4)^2=-5^2 meaning the center would be (-2,4) and radius -5 \n" ); document.write( "

Algebra.Com's Answer #404547 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
You have the center correct but not the radius.

\n" ); document.write( " $\"x%5E2%2By%5E2%2B4x-8y%2B13=0\"$
\n" ); document.write( "We start by completing the squares for both the x terms and the y terms. Usually this tarts with \"moving\" the constant term to the other side. Subtracting 13 from each side we get:
\n" ); document.write( " $\"x%5E2%2By%5E2%2B4x-8y+=+-13\"$

\n" ); document.write( "Then we rearrange the terms so that the x terms are together and the y terms are together:
\n" ); document.write( " $\"x%5E2%2B4x%2By%5E2-8y+=+-13\"$

\n" ); document.write( "To complete the square for the x terms we take half the coefficient of x, 4, and square it. Half of 4 is 2 and 2 squared is, coincidentally, 4. We do the same for the y term. Half of -8 is -4 and -4 squared is 16. So we will add a 4 and a 16 to each side:
\n" ); document.write( " $\"x%5E2%2B4x%2B4y%5E2-8y+%2B16=+-13%2B4%2B16\"$
\n" ); document.write( "Next we simplify the right side and rewrite the left side as binomial squares:
\n" ); document.write( " $\"%28x%2B2%29%5E2%2B%28y-4%29%5E2+=+7\"$
\n" ); document.write( "Last of all we rewrite the right side as a perfect square:
\n" ); document.write( " $\"%28x%2B2%29%5E2%2B%28y-4%29%5E2+=+%28sqrt%287%29%29%5E2\"$

\n" ); document.write( "So the center is (-2, 4) but the radius is $\"sqrt%287%29\"$ . \n" ); document.write( "

\n" );