Please help I am stuck on these two problems:

1) A searchlight is shaped like a paraboloid of revolution. If the light source is located 4 feet from the base along the axis of symmetry and the opening is 20 feet across, how deep should the searchlight be?

2) Find the equation of the parabola described. Find the two points that define the latus rectum. Vertex at (0,0); axis of symmetry the y-axis; containing the point (5,6)

What is the equation of the parabola? _________. Find the two points that define the latus rectum. The left point is _______ and the right point Is ___________.