As shown in the figure, in the rectangular coordinate plane, the image of the function y = m / X (x > 0. M is a constant) passes through a (1,4), B (a, b), where a > 1 As shown in the figure, in the rectangular coordinate plane, the image of the function y = m / X (x > 0. M is a constant) passes through a (1,4), B (a, b), where a > 1. Through point a, the x-axis vertical line is made, the perpendicular foot is C, through point B, the y-axis vertical line is made, the perpendicular foot is D, connecting ad, DC and CB (1) If the area of △ abd is 4, calculate the coordinates of point B; (2) Verification: DC ‖ AB; (3) When ad = BC, find the function analytic formula of ab

As shown in the figure, in the rectangular coordinate plane, the image of the function y = m / X (x > 0. M is a constant) passes through a (1,4), B (a, b), where a > 1 As shown in the figure, in the rectangular coordinate plane, the image of the function y = m / X (x > 0. M is a constant) passes through a (1,4), B (a, b), where a > 1. Through point a, the x-axis vertical line is made, the perpendicular foot is C, through point B, the y-axis vertical line is made, the perpendicular foot is D, connecting ad, DC and CB (1) If the area of △ abd is 4, calculate the coordinates of point B; (2) Verification: DC ‖ AB; (3) When ad = BC, find the function analytic formula of ab

1) RT: C (1,0), D (0, b), then a (1,4), M = 4, ab = 4, s △ abd = 0.5 * a (4-b) = 4, that is, 4A AB = 4a-4 = 8, so a = 3, B = 4 / 3.2) proves that the slopes of AB and DC are equal 〓 (B-4) / (A-1) = - B, and from the known, B-4 + AB = B, it proves that 3) ad = BC, that is, (B-4) ^ 2 + 1 = (A-1) ^ 2 + B ^ 2