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 &#916; A C B is maximum. Then, the area (in sq. units) of &#916; A C B , is:

Aicharya · Accepted Answer

Let the coordinates of C be t 2 , &#160; 2 t . Area of &#8710; A B C = 1 2 &#160; t 2 2 t 1 9 6 1 4 - 4 1 &#8710; = 5 6 + t - t 2 , t &#8712; - 2 , &#160; 3 d &#8710; d t = 1 - 2 t = 0 &#8658; t = 1 2 d 2 &#9651; d t 2 = - 2 , hence area is maximum at t = 1 2 &#8756; &#160; &#160; &#160; &#160; &#916; m a x = 125 4 = 31 1 4

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…

Solution