SOLUTION: Write the equation of the circle in standard form and give the center and radius. 4x^2+4y^2-4x-8y-1=0

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Question 894166: Write the equation of the circle in standard form and give the center and radius.
4x^2+4y^2-4x-8y-1=0
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
I will only take this part of the way and you can finish it:

4x%5E2-4x%2B4y%5E2-8y=1
4%28x%5E2-x%29%2B4%28y%5E2-2y%29=1

You need to Complete The Squares.
The term for x is %28-1%2F2%29%5E2=1%2F4
The term for y is %28-2%2F2%29%5E2=1

4%28x%5E2-x%2B1%2F4%29%2B4%28y%5E2-2y%2B1%29=1%2B4%281%2F4%29%2B4%2A1, note that is equivalent to adding the two square terms to both sides of the equation.

4%28x-1%2F2%29%5E2%2B4%28y-1%29%5E2=1%2B1%2B4
.
.
Now, you continue and finish.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Write the equation of the circle in standard form and give the center and radius.
4x^2+4y^2-4x-8y-1=0 


Equation of circle, in center-radius form: highlight_green%28highlight_green%28%28x+-+1%2F2%29%5E2+%2B+%28y+-+1%29%5E2+=+6%2F4%29%29

Center coordinates:  (h, k), or (highlight_green%281%2F2%29, highlight_green%281%29)

r%5E2+=+6%2F4, so radius is: sqrt%286%2F4%29, or highlight_green%28sqrt%286%29%2F2%29

You can do the check!! 



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