DISCOVER: Circle, Point, or Empty Set? Complete the squares in the general equation x2+ax+y2+by+c=0, and simplify the result as much as possible. Under what conditions on the coefficients a, b, and c does this equation represent a circle? A single point? The empty et? In the case in which the equation does represent a circle, find its center and radius.

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DISCOVER: Circle, Point, or Empty Set? Complete the squares in the general equation x2+ax+y2+by+c=0, and simplify the result as much as possible. Under what conditions on the coefficients a, b, and c does this equation represent a circle? A single point? The empty et? In the case in which the equation does represent a circle, find its center and radius.

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