Solve the below:
Q1. Find the equation of a parabola whose vertex is (0,0) and directrix is the line y=3.
Q2. Find the vertex, focus, and directrix of (x-2)^2=12(y+1). Find the latus rectum and graph the parabola, making sure that all points and axis are labeled.
Q3. Find the equation of the ellipse whose center is the origin and has a vertex at (0,5) and a focus at (0,3).