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A cross section of a reflector of a television satellite dish is a parabola
that measures 5 ft across with a depth of 2 ft. How far from the vertex should the receiving antenna be placed?
A. 0.3125 ft
B. 0.78125 ft
C. 0.2500 ft
D. 1.25 ft
E. 0.625 ft
F. 1.8125 ft
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Place the origin of the coordinate system at vertex of the parabola.
Use the vertex form equation of this parabola
y = . (1)
At x = 2.5 ft, we are given y = 2 ft. So, this vertex equation takes the form
2 = , which gives a = = = .
So, equation (1) is
y = . (2)
For the parabola with equation y = , the distance from the vertex to the focus is
f = .
In our case, the distance from the vertex to the focus is = cm = 0.78125 ft.
ANSWER. The distance from the vertex to the focus, where the filament should be placed, is 0.78125 ft.
Option (B).
Solved.