If a light has a diameter of 36 inches at its opening, what is the depth of the light if a lightbulb is 6 inches from the vertex.

Answer 1

I will assume that your light is parabolic and the bulb is placed at its focal point

The standard form of the equation with vertex at the origin and focal point (p,0) is
y^2 = 4px

so you have a focal point of (6,0)
then y^2 = 24x is our equation

if the diameter is 36 inches, the y values are ± 18
so, ....
18^2 = 24x
x = 324/24 = 13.5 inches