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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

APPLICATIONS

Satellite Dish A reflector for a satellite dish is parabolic in cross section, with the receiverat 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?

Chapter 12.1, Problem 62E, APPLICATIONS Satellite Dish A reflector for a satellite dish is parabolic in cross section, with the

To determine

To Find:

The distance between the receiver and vertex of parabolic reflector.

Explanation

Given:

A reflector for a satellite dish is parabolic in cross section, with the receiver at the focus F is shown in figure (1).

Figure (1)

The depth of reflector is 1 ft. and has width of 20 ft. from rim to rim.

Concept:

The general equation of a parabola with vertical axis where vertex V(0,0) and focus at F(0,p) is given by,

x2=4py …… (1)

Where y=p is the directrix.

1) If p<0, then parabola opens downward.

2)If p>0, then parabola opens upward.

Width of a parabola is given by |2x|.

Calculation:

Since, given parabola is drawn with vertical axis, the general equation will be given as,

x2=4py

As the parabola opens upward, p>0

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