# Thread: [SOLVED] Need Help with a Hyperbola Problem

1. ## [SOLVED] Need Help with a Hyperbola Problem

Simple question that I can't seem to find an answer to anywhere else on the net:

If I know the distance from the focus to the vertex of a hyperbola, is it possible to find the equation of the hyperbola, assuming the center is at (0,0) on a Cartesian plane? If yes, how do you do so?

If you'd like to use my numbers to help me out, the context of the problem goes as such: I need to calculate the velocity "at infinity" of a spacecraft with a hyperbolic orbit, but doing so requires me to know the distance from the vertex to the center (commonly shown as "a"). The given information only lets me know that the periapsis radius (distance from the focus to the vertex) is 1937 km.

Thanks for any help!

2. Never mind, I realized I was missing the point of the problem. I'm pretty sure the answer to my own question is no, though, the distance from the focus to the vertex is not specific for an individual hyperbola, (i.e. hyperbolas of different equations can have the same focus to vertex length). Feel free to still correct me if I'm wrong.