SOLUTION: find the radius x^2-6x+y^2+4y = 36

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Question 117007: find the radius
x^2-6x+y^2+4y = 36
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-6x%2By%5E2%2B4y=36 Start with the given equation
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%28-6%2F2%29%5E2=%28-3%29%5E2=9 Take half of the x coefficient -6 and square it.

x%5E2-6x%2B9%2By%5E2%2B4y=36%2B9 Add this result to both sides


x%5E2-6x%2B9%2By%5E2%2B4y=45 Combine like terms


%284%2F2%29%5E2=%282%29%5E2=4 Take half of the y coefficient 4 and square it.

x%5E2-6x%2B9%2By%5E2%2B4y%2B4=45%2B4 Add this result to both sides


x%5E2-6x%2B9%2By%5E2%2B4y%2B4=49 Combine like terms
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%28x%5E2-6x%2B9%29%2B%28y%5E2%2B4y%2B4%29=49 Group like terms


%28x-3%29%5E2%2B%28y%2B2%29%5E2=49 Factor



Since the general equation of a circle is

%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2

we can see that r%5E2=49 with means r=7. So the radius is 7