# Limit of a point on a curve

Calculus Level 5

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 $$\displaystyle \lim_{n \to \infty } (n \cdot d_n)$$.

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