Question

How do I find the equation of a hyperbola using its vertices and foci

Answer 1

determine the center of hyperbola by finding the center point between vertexes.

determine which direction the thing opens; open up, +y ... open to the side, +x

then it amounts to finding the asymptotes needed to assess the underside of the x and y parts.

Answer 2

the distance from center to a vertex is conventionally defined as 'a'

the distance from center to a focus is conventionally defined as 'c'

and a hyperbola uses the setup: a^2 + b^2 = c^2, and we simply need to know a^2 and b^2 to write the equation with.