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Chapter 10: Q. 63 (page 644)

A satellite dish is shaped like a paraboloid of revolution. The signals that emanate from a satellite strike the surface of the dish and are reflected to a single point, where the receiver is located. If the dish is 10 feet across at

its opening and 4 feet deep at its center, at what position should the receiver be placed?

Short Answer

Expert verified

The position of receiver will be 1.562 ft .

Step by step solution

01

Step 1. Given information .

Consider the given distance from the base and depth .

02

Step 2. Equation of parabola used.

The equation of the parabola is x2=4ay,the vertex of the parabola is at origin and its focus is on the y positive axis .

Here ,x=102=5and a=4.

Substitute the values in equation of parabola .

x2=4ay52=4路4路yy=2516y=1.562

Therefore the receiver should be located 1.562 ft from the base of the dish .

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