Find the equations of the hyperbola satisfying the given conditions :Foci `(+-4,0)`, the latus rectum is of length 12

Explanation

To find the equation of the hyperbola given the foci and the length of the latus rectum, we can follow these steps:

### Step 1: Identify the center and orientation of the hyperbola
Since the foci are given as \((\pm 4, 0)\), this indicates that the hyperbola is centered at the origin \((0, 0)\) and opens horizontally. The general form of the equation for a hyperbola that opens horizontally is:

\[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \]
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