Question

A parabolic microphone used on the sidelines of a professional football game uses a reflective dish 24 in. wide and 6 in. deep. How far from the bottom of the dish should the microphone be placed

Answer 1

Answer : 6 in

A parabolic microphone used on the sidelines of a professional football game uses a reflective dish 24 in. wide and 6 in. deep

Parabolic microphone is in the form of vertical parabola

Vertex at the origin so vertex is (0,0)

24 inch wide so its 12 inches  on the right and 12 inches on the left

So coordinate on parabola are (6,12)  and (6,-12)

for vertical parabola we use equation y^2 = 4ax

WE use any one of the point and find out 'a'

Lets plug in (6,12)

$y^2 = 4ax$

$12^2 = 4a(6)$

144= 24a

Divide both sides by 24

a= 6

So microphone is 6 inches away

Answer 2

The answer is a 6 inches away