Find the vertices, eccentricity, foci, equation of directrices length of latus rectum for the hyperbola `3y^(2)-x^(2)=27`.

Explanation

To solve the problem of finding the vertices, eccentricity, foci, equation of directrices, and length of latus rectum for the hyperbola given by the equation \(3y^2 - x^2 = 27\), we will follow these steps:

### Step 1: Convert the hyperbola to standard form

The given equation is:
\[ 3y^2 - x^2 = 27 \]
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