If a curve is represented by the equation- 4 x^2+4 y^2-8x+24y+7=0 is, (X,Y)then,
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By partial differentiation any curve equation with respect to x and y , and solving the resultant equation we get the center of that curve. Now, by partial differentiating the equation w.r.t x and y , we get, X=1, Y=-3 .Therefore the center is X=1 and Y=-3