Question

If a ≠ b ≠ c, prove that the points (a, a²), (b, b²), (c, c²) can never be collinear.

Answer 1

 Let A(a, a²), B(b, b²) and (c, c²) be the given points.

Area of ΔABC

i.e., the points are collinear if a=b=c

Hence, the points can never be collinear if a ≠ b ≠ c.