If the area (in sq. units) bounded by the parabola y 2 = 4 λ x and the line y = λ x ,   λ > 0 , is 1 9 , then λ is equal to

Step-by-step solution

The given equations are y 2 = 4 λ x and y = λ x Using above equations, we can write λ x 2 = 4 λ x ⇒ λ 2 x 2 - 4 λ x = 0 ⇒ λ x λ x - 4 = 0 ⇒ x = 0   &   x = 4 λ Area = 1 9 = ∫ 0 4 λ 4 λ x - λ x d x ⇒ 4 λ x 3 2 3 2 - λ x 2 2 0 4 λ = 1 9 ⇒ λ = 24 Hence, the required value is 24 .