A cross-section of a parabolic reflector and bulb is located at the focus is 16cm.find the equation of the parabola and the diameter of the opening (R,S),11cm from the vertex

Answer 1

Your reflector is just a parabola revolved about its axis.
Recall that the parabola

x^2 = 4py has
latus rectum = 2p
focus at (0,p)
vertex at (0,0)

So, your parabola has p=8, making its equation

x^2 = 32y

Now you want 2x where y=11

That will be 2√(32*11) = 8√22