Find the vertex, axis, directrix, focus, latus rectum and the tangent at vertex for the parabola `9y^(2)-16x-12y-57=0`

Explanation

To solve the problem step by step, we will analyze the given equation of the parabola and extract the required components: vertex, axis, directrix, focus, latus rectum, and tangent at the vertex.

### Given Equation:
The equation of the parabola is:
\[ 9y^2 - 16x - 12y - 57 = 0 \]

### Step 1: Rearrange the Equation
First, we rearrange the equation to isolate the terms involving \(y\):
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