Question

A parabolic microphone used on the sidelines of a professional football game uses a reflective dish 24 inches wide and 5 inches deep. How far from the bottom of the disk should the microphone be placed?

a.) 6.8 in
b.) 7 in
c.) 7.2 in
d.) 7.4 in

Answer 1

If we put the parabolic microphone into the coordinate system with the vertex at the origin and facing to the right, the equation of the parabola would have the form:
y² = 4ax
where a is the distance between the vertex and the focus
From the problem we are given with the coordinates:
(5,12) and (5, -12)
Substituting any of the coordinates to solve for a:
12² = 4a(5)
a = 7.2 in

The answer is:
c.) 7.2 in