Question

A parabolic microphone used on the sidelines of a professional football game uses a reflective dish 24 inches wide and 6 inches deep. How far from the bottom of the disk should the microphone be placed?
a.) 6 in
b.) 5.8 in
c.) 5.2 in
d.) 4 in

I tried solving this on my own but I am getting lost. Please help?

Answer 1

If we place the vertex of the parabola at (0,0), then since y=6 when x=12, we have

y = 1/24 x^2

Recall that the parabola

x^2 = 4py has its focus at (0,p)

So, we have p=6