A calculus problem by Ankit Nigam

Calculus Level 3

A variable triangle ABC in the xy plane has its orthocentre at vertex 'B', a fixed vertex 'A' at the origin and the third vertex 'C' restricted to lie on parabola y = 1+\(\frac{7x^{2}}{36} \). The point B starts at the point (0,1) at time t=0 and moves upward along the y axis at a constant velocity of 2cm/sec. How fast is the area of the triangle increasing when t=7/2 sec?

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