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) is1937 km.

Thanks for any help!