Find the coordinates of the foci and the vertices, the eccentricity, the length of the latus rectum of the hyperbolas:
(i) `(x^2)/9-(y^2)/(16)=1` (ii) `y^2-16 x^2=16`

Explanation

Let's solve the problem step by step for both hyperbolas.

### (i) For the hyperbola \(\frac{x^2}{9} - \frac{y^2}{16} = 1\):

1. **Identify the standard form**:
The equation is in the form \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\).
Here, \(a^2 = 9\) and \(b^2 = 16\).

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