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?
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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) (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) (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:
Group the terms:
Subtract 80 from both sides.
} Complete the square in x and y.
Simplify.
Compare with standard form above:
, ,
The coordinates of the center: (-10, 8)
Length of radius: = approx.
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