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Definition: Let (h, k) be a given point in the xy-plane and r > 0 a given positive real number. The circle of radius r centered at (h, k) is precisely all of the solutions (x,y) of the equation (x − h)^2 + (y − k)^2 = r^2; i.e., the circle is the graph of this equation, where h and k are the x- and y-coordinates of the center of the circle.
Source: "Precalculus" by David H. Collingwood and K. David Prince at the University of Washington
Example: A circle centered at the origin with a radius of 4 would be notated as: (x-0)^2 + (y-0)^2 = 16 Another circle centered at the point (6,2) with a radius of 2 would be notated as: (x-6)^2 + (y-2)^2 = 4