Assignment:
Find the equation of the parabola:
1. Vertex at (-2, 3), Focus at (-4, 3)
2. Vertex at (2, 4), directrix at x = -3
3. Vertex at (-1, -2), axis vertical and passing (3, 6)
4. Directrix = 4y, focus at (3, 0)
5. Axis horizontal, parabola passing through: (1, 1), (1, -3), and (-2, 0)
6. Latus rectum joining the points (2, 5) and (2, -3) & opening to the left.
7. Axis at x = 0, latus rectum 4, directrix y = 3, opening down.
Provide complete and step by step solution for the question and show calculations and use formulas.