Hi All

I'm hoping someone can help me on this:

I have a piece of paper. (200mm in length) I take the two sides of the paper and push them closer to each other until they are 50mm apart. How "high" is the hyperbola's peak?

Basically, if I have two points: A(0, 0) and B(200, 0) with a straight line running between, and I shift point B closer to A so that B(50, 0), yet the length of the curve now still connecting A and B is at 200mm, how do I calculate the "peak" of the hyperbola in coordinates similar to A and B?

Is there a function / formula / equation to work this out? I hope that whoever is reading this understands the question...

Thanks in advance, and as always: Any help is greatly appreciated!