# Thread: complete the square

1. ## complete the square

x^2+y^2=2ay

please explain step by step.
Thanks

2. What you can do is take the 2ay to the other side and add a^2 to both sides:

$x^2 + y^2 - 2ay + a^2 = a^2$

The reason we do this is because a perfect square has coefficients of 1-2-1, so we take the coefficient of the second leading y term and divide it by 2, then square it and add/subtract it to complete the square.

$x^2 + (y-a)^2 = a^2$

Which looks like a circle to me.