An expression that can be represented in the form (x - a)^2 + (y -b)^2 = r^2 is the equation of a circle with center at (a, b) and radius r. It has to be of the form given and not just one that has x^2 and y^2 terms as even the equation of an ellipse has x^2 and y^2.

The given equation x^2 − 4x + y^2 − 2y = 11

=> x^2 - 4x + 4 + y^2 - 2y + 1 = 11 + 4 + 1

=> (x - 2)^2 +( y - 1)^ = 4^2

This is a circle with center (2,1) and radius 4

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