SOLUTION: The graph of the function x^2+y^2+20x-16y+80=0 is a circle. What are the coordinates of the center and the length of the radius?

Algebra ->  Circles -> SOLUTION: The graph of the function x^2+y^2+20x-16y+80=0 is a circle. What are the coordinates of the center and the length of the radius?       Log On


   

Question 392026: The graph of the function x^2+y^2+20x-16y+80=0 is a circle. What are the coordinates of the center and the length of the radius?
Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The graph of the function x^2+y^2+20x-16y+80=0 is a circle. What are the coordinates of the center and the length of the radius?
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Complete the square:
x^2+20x+100 + y^2-16y+64 = -80+100+64
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Factor:
(x+10)^2 + (y-8)^2 = 84
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Center: (-10,8)
Radius: sqrt(84) = 2sqrt(21)
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Cheers,
Stan H.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Find the center and length of radius of the circle:
Get the equation into standard form for a circle: %28x-h%29%5E2%2B%28y-k%29%5E2+=+r%5E2
x%5E2%2By%5E2%2B20x-16y%2B80+=+0 Group the terms:
%28x%5E2%2B20x%29%2B%28y%5E2-16y%29%2B80+=+0 Subtract 80 from both sides.
%28x%5E2%2B20x%29%2B%28y%5E2-16y%29+=+-80} Complete the square in x and y.
%28x%5E2%2B20x%2B100%29%2B%28y%5E2-16y%2B64%29+=+100%2B64-80 Simplify.
%28x%2B10%29%5E2+%2B+%28y-8%29%5E2+=+84 Compare with standard form above:
h+=+-10, k+=+8 , r+=+sqrt%2884%29
The coordinates of the center: (-10, 8)
Length of radius: sqrt%2884%29 = 9.165approx.