Answer:
The depth of the reflector is 0.84 feet
Step-by-step explanation:
(See the figure below)
The equation of a parabola centered at the origin with an axis of symmetry on y-axis is:
[tex] x^{2}=4py [/tex] (1)
With p the distance from the origin to the focus using p=6, the equation (1) of the parabola becomes:
[tex] x^{2}=4(6)y=24y [/tex] (2)
Note that the point B is on the parabola, so this point should satisfy the parabola equation (2) that allow us to use the value x=4.5 to find the y value associated to it, that it is the depth (h) of the reflector:
[tex](4.5)^{2}=24y [/tex], solving for y
[tex]y=\frac{(4.5)^{2}}{24}\approx0.84\,ft [/tex]
