Question 1204941
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The other tutors have great answers. I'll extend their scratch work to complete the square for the y term, and use it to determine the center and radius of this circle.


In the fourth step shown below, I add and subtract 4.
The 4 comes from taking half of the y coefficient, and then squaring it.


x^2 + y^2 = 4y 
x^2 + y^2 - 4y = 0 
x^2 + (y^2 - 4y) = 0 
x^2 + (y^2 - 4y + 4 - 4) = 0 
x^2 + (y^2 - 4y + 4) - 4 = 0 
x^2 + (y-2)^2 - 4 = 0 
x^2 + (y-2)^2 = 4


Compare that to the circle template (x-h)^2 + (y-k)^2 = r^2
We determine that h = 0, k = 2, r = 2
This circle has its center at (h,k) = (0,2) and has radius r = 2. 
Desmos can be used to confirm the answer
<a href="https://www.desmos.com/calculator/os2lf1m92p">https://www.desmos.com/calculator/os2lf1m92p</a>
Click the wrench icon in the upper right corner to go from cartesian mode to polar mode. 


Even though it appears your teacher may not be asking for the circle's center and radius, it's still good practice to be able to find it.
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