The equation of the hyperbola with vertices `(3,0)` and `(-3,0)` and semi-latursrectum `4`, is given by

Options

A. `4x^(2)-3y^(2)+36=0`
B. `4x^(2)-3y^(2)+12=0`
C. `4x^(2)-3y^(2)-36=0`
D. none of these

Explanation

To find the equation of the hyperbola with given vertices and semi-latus rectum, we will follow these steps:

### Step 1: Identify the vertices and the value of 'a'
The vertices of the hyperbola are given as (3, 0) and (-3, 0). The distance from the center (0, 0) to either vertex is 'a'.

Thus,
\[ a = 3 \]

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