SOLUTION: What is the radius of the circle 2x^2+2y^2-8x+16y-32=0? I think it is 6???????

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Question 139830: What is the radius of the circle 2x^2+2y^2-8x+16y-32=0? I think it is 6???????
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2%2B2y%5E2-8x%2B16y-32=0 Start with the given equation


2x%5E2-8x%2B2y%5E2%2B16y-32=0 Rearrange the terms


2x%5E2-8x%2B2y%5E2%2B16y=%2B32 Add 32 to both sides


2%28x-2%29%5E2-8%2B2y%5E2%2B16y=%2B32 Complete the square for the x terms


2%28x-2%29%5E2-8%2B2%28y%2B4%29%5E2-32=%2B32 Complete the square for the y terms


2%28x-2%29%5E2%2B2%28y%2B4%29%5E2-40=%2B32 Combine like terms


2%28x-2%29%5E2%2B2%28y%2B4%29%5E2=%2B32%2B40 Add 40 to both sides


2%28x-2%29%5E2%2B2%28y%2B4%29%5E2=72 Combine like terms


2%28%28x-2%29%5E2%2B%28y%2B4%29%5E2%29=72 Factor out the common term 2


%28x-2%29%5E2%2B%28y%2B4%29%5E2=36 Divide both sides by 2



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Notice how the equation is now in the form %28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2. This means that this conic section is a circle where (h,k) is the center and r is the radius.
So the circle has these properties:

Center: (2,-4)

Radius: r=sqrt%2836%29=6



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Answer:

So the radius of the circle is 6 units