Question

Two lines draw through the point P(4, 0) divide the area bounded by the curves y = √2 sin(πx/4) and x-axis, between the line x = 2 and x = 4, in to three equal parts. Sum of the slopes of the drawn lines is equal to

(A) -2√2/π

(B) -√2/π

(C) -2/π

(D) -4√2/π

Answer 1

Answer is (A) -2√2/π

See Fig.. 

Area bounded by y = √2. sin(πx/4) and x-axis between the lines x = 2 and x = 4,

= 4√2/π sq. units

Let the drawn lines are L₁: y - m₁(x - 4) = 0 and L₂: y - m₂(x - 4) = 0, meeting the line x = 2 at the points A and B, respectively.

Clearly A = (2, -2m₁); B = (2, -2m₂) (Fig.).

Now