Application Of Derivatives

Let $f: R \rightarrow R$ be a bijection. A curve represented by $y=f(x)$ is such that $f^{\prime}(x)>0 \forall x \in \mathbf{R}$. The tangent and normal drawn at $P(\alpha, 1)$ on the curve cuts the $X$-axis at $A, B$ respectively and $C$ is the foot of the perpendicular from $P$ onto the $X$-axis. If $P(\alpha, 1)$ is such a point that $A C+C B$ is minimum, then the tangent at $P$ is parallel to the line