Find the equations of the hyperbola satisfying the given conditions :Foci `(+-3sqrt(5),0)`, the latus rectum is of length 8.

Explanation

To find the equation of the hyperbola given the conditions that the foci are at \((\pm 3\sqrt{5}, 0)\) and the length of the latus rectum is 8, we can follow these steps:

### Step 1: Identify the standard form of the hyperbola
Since the foci are on the x-axis, the standard form of the hyperbola is given by:
\[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \]

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