Let y=3x-8 be the equation of the tangent at the point (7, 13 ) lying on a parabola whose focus is at (-1,-1). Find the equation of directrix and the length of the latus rectum of the parabola.

Explanation

To solve the problem step-by-step, we will find the equation of the directrix and the length of the latus rectum of the parabola given the focus and the tangent line.

### Step 1: Identify the given information
We have:
- The equation of the tangent line: \( y = 3x - 8 \)
- The point of tangency: \( (7, 13) \)
- The focus of the parabola: \( (-1, -1) \)

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