Limit of a point on a curve

Calculus Level 5

For each positive integer nn,consider the point PP,with x\displaystyle{x}-coordinate nn on the curve y2x2=1\displaystyle{y^2 - x^2 = 1}.If dn\displaystyle{d_n} represents the shortest distance from point P to the line y=x\displaystyle{y=x},then find limn(ndn) \displaystyle \lim_{n \to \infty } (n \cdot d_n).

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