As shown in the figure, if the line y = KX + B (K ≠ 0) intersects the X axis at point a (5 / 2,0), and the hyperbola y = m / X (m ≠ 0) intersects at point B in the second quadrant, and OA = ob The area of △ OAB is 5 / 2 1. Find the analytic formula of straight line AB and hyperbola, 2. If the other intersection of the straight line AB and the hyperbola is the point D, find the value of s △ BOC

As shown in the figure, if the line y = KX + B (K ≠ 0) intersects the X axis at point a (5 / 2,0), and the hyperbola y = m / X (m ≠ 0) intersects at point B in the second quadrant, and OA = ob The area of △ OAB is 5 / 2 1. Find the analytic formula of straight line AB and hyperbola, 2. If the other intersection of the straight line AB and the hyperbola is the point D, find the value of s △ BOC

1. S = 1 / 2 * 5 / 2H = 5 / 2 h = 2, substituting y = 2 into y = KX + B, x = (2-B) / K B ((2-B) / K, 2)
Because ob = OA = 5 / 2, so (2-B) ^ 2 / K ^ 2 + 4 = 25 / 4, that is, (b-2) ^ 2 = 9 / 4 (k ^ 2), and - B / k = 5 / 2, so 5 / 4,
k=-1/2 B(-3/2,2)
So the analytic formula of AB is y = - 1 / 2x + 5 / 4, and the hyperbola is y = - 3 / X
2. - 1 / 2x + 5 / 4 = - 3 / x, x = 4 or x = - 3 / 2, so D (4, - 3 / 4)
S-BOD=1/2*5/4*3/2+1/2*5/4*5/2+1/2*5/2*3/4=55/16