reduce the equation x^2+y^2+8x-6y-25=0 to the form AX^2+BY^2=K^2 by shifting the origin

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Let the origin be shifted to the point (h,k) axes remaining parallel to the originalaxes.If the coordinates (x,y) of any point on the given curve change to (X,Y), thenx=X+h and y=Y+kSubstituting for x and y in the given equation, the transformed equation isX+h2+Y+k2+8X+h-6Y+k-25=0X2+h2+2Xh+Y2+k2+2Yk+8X+8h-6Y-6k-25=0X2+Y2+2h+8X+2k-6Y+h2+k2+8h-6k-25=0    ...(1)Since the given equation is to be reduced to the form AX2+BY2=K, the coordinates of X and Y are zero.2h+8=0 and 2k-6=0h=-4 and k=3 and thenh2+k2+8h-6k-25=16+9-32-18-25=-50hence, on shifting the origin to the point -4,3 the given equation reduces to X2+Y2=50 
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