On ∴y=-2, the coordinate of point B is (-8, -2), and ∵ hyperbola y = k/x (k >; 0)
And the straight line y= 1/4x.
The coordinates of the intersection points A and B ∴A and B with respect to the origin ∴ point A are (8,2), and point A is on the hyperbola y = k/x (k >); 0) Up ∴k=8*2= 16
(2) If B is the midpoint of CD, the area of the quadrilateral OBCE is 4, and the coordinates of point B are (-2n, -n/2).
∴ k = (-2n) * (-n/2) = n 2 ∴ The coordinates of point E are (-n,-n).
The area of the quadrilateral OBCE is 4 ∴1/2 * 2n * (n/2+n)-1/2 * n * n = 4 ∴ n = 2.
The coordinate of point ∴c is (-4, -2), the coordinate of point ∴ M is (2, 2), and the analytical formula of line ∴ CM is y=2/3x+2/3.
(3) If the coordinate of point A is (t, 1/4*t), the coordinate of point M is (m, t 2/4m) and the coordinate of point B is
(-t,-1/4*t), and the analytical formula of linear AM is y =-t 2/4m * x+(t 2+TM)/4m.
Analytical formula of line BM y = t 2/4m * x+(t 2-TM)/4m.
The coordinates of point P are (0, (t 2+tm)/4m), and the coordinates of point Q are (0, (t 2-tm)/4m).
p=ma/mp=(t^2/4m- 1/4*t)/((t^2+tm)/4m-t^2/4m)=(t-m)/m
q=mb/mp=(t^2/4m+ 1/4*t)/((t^2+tm)/4m-t^2/4m)=(t+m)/m
p-q=(t-m)/m-(t+m)/m=-2