The full question is this: Point P on curve y = cosh x is such that its perpendicular distance from the line y = x is a minimum. Show P's coordinates are (ln(1 + root 2), root 2).

I am completely at a loss as to what to do. I cannot find any example online for a similar question for a hyperbolic function, and the similar questions I have found aren't that well explained. This question is from an old textbook from an old specification for Further Maths. So it seems I may never learn the information I need to solve this, or I just haven't learnt it yet. All examples online include a parabola, which seems a lot simpler than a hyperbolic. Any help appreciated.