   Chapter 10, Problem 25RE

Chapter
Section
Textbook Problem

Satellite Antenna A cross section of a large parabolic antenna is modeled by the graph of y = x 2 / 200 , − 100 ≤ x ≤ 100 The receiving and transmitting equipment q is positioned at the focus.(a) Find the coordinates of the focus.(b) Find the surface area of the antenna.

(a)

To determine

To calculate: The coordinate points of the focus when a cross section of a large parabolic antenna is modelled by the graph of y=x2200, the interval is 100x100 and the position of the receiving and transmitting equipment is at the focus.

Explanation

Given:

The function is y=x2200, the interval is 100x100.

Formula used:

The standard equation of a parabola with vertical axis is:

(xh)2=4p(yk)

Focus is given by (h,k+p)

Calculation:

Consider the given equation:

y=x2200

The standard equation of a parabola with vertical axis is:

(xh)2=4p(yk)

Write the given equation in the standard form

(b)

To determine

To calculate: The surface area of the antenna when a cross section of a large parabolic antenna is modelled by the graph of y=x2200, the interval is 100x100 and the position of the receiving and transmitting equipment at the focus.

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