Find the equation of the hyperbola with foci `(0,+-3)`and vertices `(0,+-(sqrt(11))/2)`

Explanation

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

### Step 1: Identify the values of \( a \) and \( c \)
The foci are given as \( (0, \pm 3) \) and the vertices are given as \( (0, \pm \frac{\sqrt{11}}{2}) \).

From the vertices, we can determine:
- The distance from the center to a vertex is \( a \).
- Thus, \( a = \frac{\sqrt{11}}{2} \).
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