Given: Equation of the curve 
……….(i)
Let 
be the required point on curve (i)
According to the question, 
……….(ii)
From eq. (i), 
[From eq. (ii)]
Taking 
Required point is (4, 11).
Taking 
Required point is 
.
A particle moves along the curve Find the points on the curve 6y=x^3+2at which the y-coordinate is changing 8 times as fast as the x-coordinate.
A particle moves along the curve Find the points on the curve 6y=x^3+2at which the y-coordinate is changing 8 times as fast as the x-coordinate.