SOLUTION: find the center and radius of y^2+x^2+9y-6x-10=0

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Question 175425: find the center and radius of y^2+x^2+9y-6x-10=0
Found 2 solutions by Mathtut, stanbon:
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
y^2+x^2+9y-6x-10=0
:
we need to complete the squares on the x and y terms
:
x%5E2-6x%2B9%2By%5E2%2B9y%2B%2881%2F4%29-9-%2881%2F4%29-10=0adding and subtracting same terms to complete the square and to keep this an equivalent equation
:
%28x-3%29%5E2%2B%28y%2B9%2F2%29%5E2=10%2B9%2B%2881%2F4%29completing square
:
%28x-3%29%5E2%2B%28y%2B9%2F2%29%5E2=157%2F4combining terms on right
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radius is square root of the right side in this form.
:
so the center is (3,-9/2) and the radius is sqrt%28157%2F4%29=6.26

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
find the center and radius of y^2+x^2+9y-6x-10=0
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Complete the square on the x-terms and on the y-terms:
[x^2 - 6x + ?] + [y^2 + 9y + ?] = 10
[x^2 -6x + 9] + [y^2 + 9y + (9/2)^2] = 10 + 9 + (9/2)^2
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(x-3)^2 + (y+(9/2))^2 = 23.5
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Center: (3,(-9/2))
Radius: sqrt(23.5)
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Cheers,
Stan H.