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a satellite dish has a shape 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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It is a standard problem of this kind. The feature is
that in this problem the symmetry line is parallel to x-axis,
while usually in such problems the symmetry line is parallel to y-axis.
So, I will adapt a standard solution to this case.
For solving such problems, write an equation of the parabola in the cross-section
in the form
x = . (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 = .
It gives the equation of the parabolic section
x = , or x = . ANSWER
Solved.