The portion of the line 4 x + 5 y = 20 in the first quadrant is trisected by the lines L 1 and L 2 passing through the origin. The tangent of an angle between the lines L 1 and L 2 is :

Step-by-step solution

Using section formula Co-ordinates of A = 1 × 5 + 2 × 0 1 + 2 , 1 × 0 + 2 × 4 1 + 2 = 5 3 , 8 3 Co-ordinates of B = 2 × 5 + 1 × 0 1 + 2 , 2 × 0 + 1 × 4 1 + 2 = 10 3 , 4 3 Slope of OA = m 1 = 8 3 - 0 5 3 - 0 = 8 5 Slope of OB = m 2 = 4 3 - 0 10 3 - 0 = 2 5 We know that, tan θ = m 1 - m 2 1 + m 1 m 2 ⇒ tan θ = 6 5 1 + 16 25 ⇒ tan θ = 30 41