Find the equation of the hyperbola whose vertices are `(0,+-3)` and the foci are `(0,+-5).`

Explanation

To find the equation of the hyperbola with the given vertices and foci, we can follow these steps:

### Step 1: Identify the center, vertices, and foci
The vertices are given as (0, ±3), which means the center of the hyperbola is at (0, 0). The vertices indicate that the distance from the center to each vertex (denoted as 'a') is 3. Thus, we have:
- Center: (0, 0)
- Vertices: (0, 3) and (0, -3)
- Distance a = 3

...