Suppose $a, b \in \mathbf{R}$ are such that the points $(a, b),\left(a^2, b^2\right)$, and $\left(a^3, b^3\right)$ in the coordinate plane are distinct, collinear, and the line passing through these points is not parallel to the $y$-axis. Then, for all such choices of $(a, b)$, the slope of the line passing through these three points can take

• A

  exactly three values.
• B

  infinitely many values.
• Correct answer
  C

  exactly two values.
• D

  exactly one value.

Hence, the correct answer is option: 'C'.