Find the vertices, eccentricity foci, rquation of directrices and length of latus rectum of the hyperbola `9x^(2)-25y^(2)=225`.

Explanation

To solve the problem of finding the vertices, eccentricity, foci, equation of directrices, and length of the latus rectum of the hyperbola given by the equation \(9x^2 - 25y^2 = 225\), we will follow these steps:

### Step 1: Convert the hyperbola to standard form
We start with the equation:
\[ 9x^2 - 25y^2 = 225 \]
To convert it to standard form, we divide the entire equation by 225:
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