For each positive integer $n$,consider the point $P$,with $\displaystyle{x}$-coordinate $n$ on the curve $\displaystyle{y^2 - x^2 = 1}$.If $\displaystyle{d_n}$ represents the shortest distance from point **P** to the line $\displaystyle{y=x}$,then find $\displaystyle \lim_{n \to \infty } (n \cdot d_n)$.