Show that `3x^(2) - 3y^(2) - 18x + 12y + 2 = 0` represents a rectangular hyperbola. Find its centre foci and eccentricity.

Explanation

To show that the equation \(3x^2 - 3y^2 - 18x + 12y + 2 = 0\) represents a rectangular hyperbola and to find its center, foci, and eccentricity, we will follow these steps:

### Step 1: Rewrite the Equation
Start by rewriting the given equation:
\[ 3x^2 - 3y^2 - 18x + 12y + 2 = 0 \]
Divide the entire equation by 3 to simplify:
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