Concept explainers
Satellite Dish A reflector for a satellite dish is parabolic in cross section, with the receiver at the focus F. The reflector is 1 ft deep and 20 ft wide from rim to rim (see the figure). How far is the receiver from the vertex of the parabolic reflector?
To find: The distance of the receiver from the vertex, located at the focus of the parabolic reflector with
Answer to Problem 54E
The distance of the receiver at the focus from the vertex of the parabola is
Explanation of Solution
Definition used:
The equation of the parabola with vertex
Calculation:
From the given diagram observe that the parabola is open upward.
Thus, the equation of the parabola is of the form
Given that the reflector is 1ft deep, 20m wide and the axis divides the 20ft wide in to two halves.
Let
Therefore, the point
When y =1 there are two points on the parabola.
Substitute y =1 in
The focal diameter is 4p.
Given that the width of the dish is
Substitute
Thus, focus of the parabola reflector is
Therefore, the receiver is at a distance of
Chapter 11 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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