Show that the three distinct points `(a^2,a) (b^2,b)` and `(c^2,c)` can never be collinear.

Explanation

Area of triangle with vertices `(a^2,a) (b^2,b)` and `(c^2,c)` is
`1/2 {a^2(b-c) + b^2(c-a) + c^2(a-b)}`
= (a-b) (b-c) (a-c)
which is never equal to zero except when a = b = c, hence the points are not collinear.