Question 1165727
.
a satellite dish has a {{{highlight(cross(shaped))}}} <U>shape</U> of a paraboloid. If the receiver of the satellite dish 
is placed at the focus 2.53 ft from the vertex, write an equation for the cross-section 
of the satellite dish. Assume that the focus is on the positive x-axis and its vertex at the origin.
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It is a standard problem of this kind. The feature is

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;that in this problem the symmetry line is parallel to x-axis,

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;while usually in such problems the symmetry line is parallel to y-axis.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;So, I will adapt a standard solution to this case.



<pre>
For solving such problems, write an equation of the parabola in the cross-section
in the form

    x = {{{(1/(4p))*y^2}}}.    (1)


The advantage of writing in this form is the fact that then "p"
is the distance from the parabola vertex to its focus.


In this problem, the value of p is given: it is 2.53 ft.


So, we substitute this value into equation (1), and we get

    x = {{{(1/(4*2.53))*y^2}}}.


It gives the equation of the parabolic section 

    x = {{{(1/10.12)*y^2}}},  or  x = {{{0.098814229*y^2}}}.    <U>ANSWER</U>
</pre>

Solved.