From a point P, tangents drawn to the ci...

From a point `P`, tangents drawn to the circle `x^2 + y^2 + x-3=0, 3x^2 + 3y^2 - 5x+3y=0 and 4x^2 + 4y^2 + 8x+7y+9=0` are of equal lengths. Find the equation of the circle through `P`, which touches the line `x+y=5` at the point `(6, -1)`.

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