Let A 4 , - 4 and B 9 , 6 be points on the parabola, y 2 = 4 x . Let C be chosen on the arc A O B of the parabola, where O is the origin, such that the area of Δ A C B is maximum. Then, the area (in sq. units) of Δ A C B , is:

Step-by-step solution

Let the coordinates of C be t 2 ,   2 t . Area of ∆ A B C = 1 2   t 2 2 t 1 9 6 1 4 - 4 1 ∆ = 5 6 + t - t 2 , t ∈ - 2 ,   3 d ∆ d t = 1 - 2 t = 0 ⇒ t = 1 2 d 2 △ d t 2 = - 2 , hence area is maximum at t = 1 2 ∴         Δ m a x = 125 4 = 31 1 4