First, we need to derive the equation of the parabola.


Standard form equation of a parabola is y = .


Since the parabola is 60 feet wide at 5 feet from its vertex, it means that y = 5 at x = 30


    5 = ,  which implies  a =  = .


Thus the standard equation of the parabola is  

             y =      (1)

under given conditions.


Next, it is well known fact that if the parabola has the form  y = ,  then the focus of the parabola is at y = 

    (see the lesson  Parabola definition, canonical equation, characteristic points and elements  at this site).


Comparing it with the equation, we get  2p = 180,  i.e.  p =  = 90.

Hence, receiver should be placed on the parabola axis at the distance of   =  = 45 feet from the vertex.