Mathematics

Problem

For each positive integer

n

, consider the point

P

with abscissa

n

on the curve

y^2 - x^2 = 1

. If

d_n

represents the shortest distance from the point

P

to the line

y = x

, then

\lim_{n \to \infty} (n \cdot d_n)

has the value equal to a. \frac{1}{2\sqrt{2}} b. \frac{1}{2} c. \frac{1}{\sqrt{2}} d. 0