In a Mahakumbh, a drone camera is moving along 3y = x^3 - 3 . When y -coordinate changes 9 times as fast as x -coordinate, it captures good quality pictures. Then one of the precise positions of the drone at that instant is

Step-by-step solution

The equation of the curve is given by 3y = x^3 - 3 . Differentiating both sides with respect to time t , we get: 3 dy dt = 3x^2 dx dt dy dt = x^2 dx dt Given that the y -coordinate changes 9 times as fast as the x -coordinate: dy dt = 9 dx dt Equating the two expressions for dy dt : x^2 dx dt = 9 dx dt Assuming dx dt 0 , we get x^2 = 9 , which gives x = 3 or x = -3 . For x = 3 , substituting into the curve equation gives 3y = (3)^3 - 3 = 24 y = 8 . The point is (3, 8) . For x = -3 , substituting into the curve equa