If the line and hyperbola x2-4y2 = 4 intersect at two points a and B, if the midpoint coordinate of line AB is (8,1), then the equation of the line is______ ．

If the line and hyperbola x2-4y2 = 4 intersect at two points a and B, if the midpoint coordinate of line AB is (8,1), then the equation of the line is______ ．

Let a (x1, Y1), B (X2, Y2), then X1 + x2 = 16, Y1 + y2 = 2, ∵ x12-4y12 = 4, x22-4y22 = 4, ∵ 16 (x1-x2) - 8 (y1-y2) = 0, ∵ KAB = Y1 − y2x1 − x2 = 2, ∵ the equation of straight line is Y-1 = 2 (X-8), that is, 2x-y-15 = 0

Given that the inclination angle of line L is equal to 3x + 4y-7 = 0, and the area of triangle enclosed by two coordinate axes is equal to 24, the equation of line L is obtained

The slope of the line 3x + 4y-7 = 0 is - 34, so the slope of the line L is - 34. Let the equation of the line l be y = - 34x + B, let y = 0, then x = 43b, let x = 0, then y = B. since the area of the line and the two axes is 24, then s = 12|b|·|43b| = 24, then B = ± 6, so the equation of the line L is y = - 34x ± 6

The intercept of the line L on the y-axis is - 1, and the inclination angle is half of that of the line l1:3x + 4y-1 = 0

The intercept of the line L on the y-axis is - 1, and the inclination angle is half of that of the line l1:3x + 4y-1 = 0
tan(α/2)=sinα/(1+cosα) = 3/5 / (1+4/5 ) = 3/ 9 = 1/3
The linear equation is y = x / 3 - 1