Final answer:
The equation of the hyperbola in standard form is x^2/3^2 - y^2/b^2 = 1.
Step-by-step explanation:
The equation of a hyperbola in standard form with vertices (h, k ± a) and foci (h, k ± c) is given by:
(x-h)^2/a^2 - (y-k)^2/b^2 = 1
In this case, since the vertices are (-3,0) and (3,0), we have h = 0 and k = 0. The distance between the vertices is 2a, so a = 3. Similarly, the distance between the foci is 2c, so c = 5. Plugging in these values, we get:
x^2/3^2 - y^2/b^2 = 1