Find the eccentricity, coordinates of the foci ,equations of directrices and length of the latus rectum of the hyperbola :`9x^2-16 y^2=144`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Write the equation of the hyperbola in standard form.
Given the equation of the hyperbola:
\[ 9x^2 - 16y^2 = 144 \]

We divide both sides by 144:
\[
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