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Chapter 10: Q. 13 (page 700)

A parabolic reflector (paraboloid of revolution) is used by TV crews at football games to pick up the referee鈥檚 announcements, quarterback signals, and so on. A microphone is placed at the focus of the parabola. If a certain reflector is 4 feet wide and 1.5 feet deep, where should the microphone be placed?

Short Answer

Expert verified

Thus, microphone should be placed 2/3 feet from the base of the reflector.

Step by step solution

01

Step 1. Given Information

Let us draw the parabola which is 4 feet wide and 1.5 deep.

The vertex of the parabola is at the origin and focus is on positive y-axis.

02

Step 2. Finding Focus

The general form of equation of parabola is x2=4ay

Since 2,1.5is on the graph, then

22=4a1.54=6aa=23

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