Broadcasters use a parabolic microphone on football sidelines to pick up field audio for broadcasting purposes. A certain parabolic microphone has a reflector dish with a diameter of 14 inches and a depth of 4 inches. If the receiver of the microphone is located at the focus of the reflector dish, how far from the vertex should the receiver be positioned?

Question

Natalya Mckee

Mathematics

30 November, 02:54

Broadcasters use a parabolic microphone on football sidelines to pick up field audio for broadcasting purposes. A certain parabolic microphone has a reflector dish with a diameter of 14 inches and a depth of 4 inches. If the receiver of the microphone is located at the focus of the reflector dish, how far from the vertex should the receiver be positioned?

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Answers (1)

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Molly Fuller · Answer 1

Given:

diameter = 14 inches

depth = 4 inches

radius = 14 / 2 = 7 inches

(x, y) → (7,4)

y = 1/4c * x²

4 = 1/4c * 7²

4 * 4c = 49

16c = 49

c = 49/16

c = 3.0625 inches

The receiver should be positioned 3.0625 inches from the vertex.