If the equation x2 + Y2 + DX + ey + F = 0 represents a circle with (2, - 4) as its center and 4 as its radius, then f=______ .

If the equation x2 + Y2 + DX + ey + F = 0 represents a circle with (2, - 4) as its center and 4 as its radius, then f=______ .

From the general equation of the circle, combined with the conditions in the problem, we can get - D2 = 2, - E2 = - 4, 12d2 + E2 − 4f = 4, the solution is d = - 4, e = 8, f = 4, so the answer is 4