The center of the circle given by the equation (x - 3)2 plus (y + 2)2 = 9 is (3,-2).
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You are describing a circle, with its center at the origin and a radius of 4 (the square root of 16)
That's the equation of a circle with its center at the origin and a radius of 8.
It is the Cartesian equation of an ellipse.
It is the equation of a parabola.
It is a quadratic equation in the one variable.