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Chapter 10: Q. 64 (page 644)

Constructing a TV Dish - A cable TV receiving dish is in the shape of a paraboloid of revolution. Find the location of the receiver, which is placed at the focus, if the dish is 6 feet across at its opening and 2 feet deep.

Short Answer

Expert verified

The location of the receiver is at 1.12 ft .

The image of satellite shown below .

Step by step solution

01

Step 1. Given information .

Consider the given distance of dish and depth .

02

Step 2. Equation of parabola used.

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

Here role="math" localid="1647017339617" x=62=3,and y=2.

Substitute the values in given formula .

x2=4ay32=4路2路aa=98a=1.12

Therefore the location of the receiver is at 1.12 ft .

03

Step 3. Plot the graph .

The graph of the receiver shown below .

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