$$\begin{gathered} Q. If a\ne b\ne c, then prove that the points \left(a,a^2\right),\left(b,b^2\right) and \left(c,c^2\right) \\ can never be collinear. \end{gathered}$$

GIVEN: If

TO PROVE: that the points can never be collinear.

PROOF:

We know three points are collinear when

Now taking three points

Also it is given that

Hence area of triangle made by these points is never zero. Hence given points are never collinear.

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