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:

Question

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:, 32, 31 3 4, 30 1 2, 31 1 4

MARKS App · Accepted Answer

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

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