Find the coordinates of the centre,vertices, foci and the equation of the directrices of the hyperbola `9x^2-16y^2=144`

Explanation

To solve the problem of finding the coordinates of the center, vertices, foci, and the equations of the directrices of the hyperbola given by the equation \(9x^2 - 16y^2 = 144\), we will follow these steps:

### Step 1: Rewrite the equation in standard form
We start with the equation of the hyperbola:
\[ 9x^2 - 16y^2 = 144 \]
To convert this into standard form, we divide both sides by 144:
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