A parabolic reflector is used by a sports broadcast engineer to amplify the conversations between football players on the field. If the reflector has the shape x = 4y², where should the microphone be placed? A) units to the right of the focus of the reflector B) units to the right of the vertex of the reflector C) 16 units to the right of the focus of the reflector D) 8 units to the right of the vertex of the reflector

Question

Quizplus · Accepted Answer

The equation given for the shape of the parabolic reflector is x = 4y^2/(4p), where p is the distance from the vertex to the focus. Therefore, we can determine the value of p by comparing the given equation with the standard form x = 4py^2:

4p = 1
p = 1/4

The vertex of the parabolic reflector is located at the point (0, 0), so the focus is located 1/4 units to the right of the vertex.

Therefore, the microphone should be placed 11 units to the right of the vertex, i.e. Choice B.

A Parabolic Reflector Is Used by a Sports Broadcast Engineer