Find the vertex, axis, focus, directrix, latus-rectum of the following parabolas. Also, draw their rough sketches. `y^2-8y-x+19=0` `4y^2+12 x-20 y+67=0` `y^=x^2-2x+3` `x^2-2y-3x+5=0`

Explanation

To solve the given problem, we will find the vertex, axis, focus, directrix, and latus rectum of each parabola step by step.

### 1. For the parabola \( y^2 - 8y - x + 19 = 0 \)

**Step 1: Rearranging the equation**
We start by rearranging the equation:
\[
y^2 - 8y = x - 19
...