Question 1206395
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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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<pre>
Place the origin of the coordinate system at vertex of the parabola.
Use the vertex form equation of this parabola 

    y = {{{ax^2}}}.        (1)


At x = 2.5 ft, we are given y = 2 ft.  So, this vertex equation takes the form

    2 = {{{a*2.5^2}}},  which gives  a = {{{2/2.5^2}}} = {{{2/6.25}}} = {{{8/25}}}.


So, equation (1) is  

    y = {{{(8/25)*x^2}}}.    (2)


For the parabola with equation y = {{{ax^2}}},  the distance from the vertex to the focus is

    f = {{{1/4a}}}.


In our case, the distance from the vertex to the focus is   {{{1/(4*(8/25))}}} = {{{25/32}}} cm = 0.78125 ft.


<U>ANSWER</U>.  The distance from the vertex to the focus, where the filament should be placed, is 0.78125 ft.  

         Option (B).
</pre>

Solved.