According to the topic, X-Y = 0 is the asymptote of a given hyperbola, which is parallel to the straight line X-Y+ 1 = 0.

∴ The distance c from point P to line X-Y+ 1 = 0 is infinitely close to the distance from X-Y = 0 to X-Y+ 1 = 0.

And this distance can be easily found as √2/2.

The maximum value of ∴c is ∴ 2/2.