If \( a \neq b \neq c \), then prove that the points \( \left(a, a^{2}\right),\left(b, b^{2}\rig...

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If \( a \neq b \neq c \), 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.
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