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Can you identify its center based on the image ?

(0,1) ?

|dw:1356930702438:dw|

And can you identify the radius of the circle ?

is it 2?

It looks like it. And @RaphaelFilgueiras provided the general equation of a circle.

Is the equation x^2 + (y + 1)^2 = 2 ?

Kk, thanks!