document.write( "Question 262418: x^2+y^2+8x+2y+13=0 Find the center and radius. If someone could explain the steps that would be great!! \n" ); document.write( "

Algebra.Com's Answer #193342 by drk(1908) $\"\"$ $\"About$

You can put this solution on YOUR website!
Here is the original equation
\n" ); document.write( "(i) $\"x%5E2%2By%5E2%2B8x%2B2y%2B13=0\"$
\n" ); document.write( "step 1 - rearrange the terms so that x's are grouped and y's are grouped together.
\n" ); document.write( "(ii) $\"x%5E2+%2B+8x+%2B+_____+%2B+y%5E2+%2B+2y+%2B+_____+=+-13+%2B+_____+%2B+_____\"$
\n" ); document.write( "the blanks are waiting for certain numbers
\n" ); document.write( "step 2 - take 1/2 of the middle terms and square it
\n" ); document.write( "(1/2)*8 = 4 -> 4^2 = 16
\n" ); document.write( "(1/2)*2 = 1 -> 1^2 = 1
\n" ); document.write( "so, we get
\n" ); document.write( "(iii) $\"x%5E2+%2B+8x+%2B+4%5E2+%2B+y%5E2+%2B+2y+%2B+1%5E2+=+-13+%2B+4%5E2+%2B+1%5E2\"$
\n" ); document.write( "notice that the blanks were filled in with the squared numbers.
\n" ); document.write( "step 3 - rewrite the x any y trinomial as a binomial squared. Also, simplify the right side to get
\n" ); document.write( "(iv) $\"%28x%2B4%29%5E2+%2B+%28y+%2B+1%29%5E2+=+4\"$
\n" ); document.write( "notice that the constant is 1/2 the middle term.
\n" ); document.write( "we have everything we need to find center and radius.
\n" ); document.write( "center = (h,k) = (-4,-1)
\n" ); document.write( "radius = 2 \n" ); document.write( "

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