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If a rectangular hyperbola (x-1)(y-2)=4 ...

If a rectangular hyperbola `(x-1)(y-2)=4` cuts a circle `x^(2)+y^(2)+2gx+2fy+c=0` at points `(3, 4), (5, 3), (2, 6) and (-1, 0)`, then the value of (g+f) is equal to

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