Tangent at P(2,8) on the curve `y=x^(3)` meets the curve again at Q.
Find coordinates of Q.

Explanation

Equation of tangent at (2,8) is y =12x -16

Solving this with `y=x^(3)`
`x^(3) -12x+16=0`
This cubic will give all points of intersection of line and curve `y=x^(3)` i.e., point P and Q . (see figure)
But since line is tangent at P so x=2 will be a repeated root of equation `x^(3) -12x +16=0` and another root will be x=h. Using theory or equations:
`"sum of roots"" "rArr " "2+2+h=0" "rArr" "h=-4`
Hence coordinates of Q are (-4,-64)