Find the standard equation of a hyperbola with center (3,-4), vertices (3,1) and (3,7) and asymptotes `y+4=pm(3)/(4)(x-3)`

Explanation

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

### Step 1: Identify the center and vertices
The center of the hyperbola is given as (3, -4). The vertices are (3, 1) and (3, 7).

### Step 2: Determine the orientation of the hyperbola
Since the x-coordinates of the vertices are the same (both are 3), the hyperbola opens vertically. Therefore, we will use the standard form for a vertically oriented hyperbola:
\[
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