For the hyperbola, `3y^(2) - x^(2) = 3`. Find the co-ordinates of the foci and vertices, eccentricity and length of the latus rectum.

Explanation

To solve the problem, we need to analyze the given hyperbola equation and extract the required parameters step by step.

### Step 1: Convert the given equation to standard form
The given hyperbola is:
\[ 3y^2 - x^2 = 3 \]

First, we rearrange this equation:
1. Multiply the entire equation by -1:
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