Please clearly show the working if willing to help.

Problem 1. 6 pts. Graph the equation. Find the vertex, focus, directrix and the exact coordinates of two other points that fall on the graph.

2y2 + 16y - 2x + 33 = 0

Problem 2. 4 pts. Find the equation of a parabola with vertex (-3, 10) and directrix y = 10.75. Graph the parabola, and find the coordinates of the y intercept (0, ?).

Problem 3. 6 pts. Graph the equation, and find the center, the vertices, and the foci. x2 - 14x + 4y2 + 80y + 445 = 0

Problem 4. 4 pts. Find the equation of an ellipse with these properties: Endpoints of the minor axis at (5, 0) and (5, -3), Major axis has length 12.

Problem 5. 8 pts. Graph the equation and find the center, vertices, foci, and equations of the asymptotes.

(𝑦 − 2)2 − 5(𝑥 + 9)2 = 25

Problem 6. 2 pts. Indicate what type of conic section is represented by the equation. (Parabola, circle, ellipse, or hyperbola)

8y2 + 224x - 7x2 - 32y - 768 = 0