SOLUTION: Please help me find the center (h,k) and radius r for the circle x^2+y^2+12x+10y+57=0

Algebra ->  Graphs -> SOLUTION: Please help me find the center (h,k) and radius r for the circle x^2+y^2+12x+10y+57=0      Log On


   

Question 226049: Please help me find the center (h,k) and radius r for the circle x^2+y^2+12x+10y+57=0
Answer by LtAurora(115) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2By%5E2%2B12x%2B10y%2B57=0
Rewrite the equation:
x%5E2%2B12x%2B___%2By%5E2%2B10y%2B___=-57%2B___%2B___
We have to complete the square, so the blanks are filled in the %28%281%2F2%29%2Ab%29%5E2
For the x: %28%281%2F2%29%2A12%29%5E2=36
So, we fill in the blank like:
x%5E2%2B12x%2B36%2By%5E2%2B10y%2B___=-57%2B36%2B___
For the y: %28%281%2F2%29%2A10%29%5E2=25
x%5E2%2B12x%2B36%2By%5E2%2B10y%2B25=-57%2B36%2B25
The x term and the y term have to be factored, but that's easy now since they are completed squares. The x-term is simply %281%2F2%29%2A12=6, and the y-term is %281%2F2%29%2A10=5. Like this:
%28x%2B6%29%5E2%2B%28y%2B5%29%5E2=4
The center is the opposite of what's in the parentheses:
(-6,-5), with a radius of 2 (because 2%5E2=4).
Good luck!