Question 1150068
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First, we need to derive the equation of the parabola.


Standard form equation of a parabola is y = {{{ax^2}}}.


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


    5 = {{{a*30^2}}},  which implies  a = {{{5/900}}} = {{{1/180}}}.


Thus the standard equation of the parabola is  

             y = {{{(1/180)*x^2}}}     (1)

under given conditions.


Next, it is well known fact that if the parabola has the form  y = {{{(1/(2p))*x^2}}},  then the focus of the parabola is at y = {{{p/2}}}

    (see the lesson  <A HREF=http://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Parabola-definition--canonical-equation--characteristic-points-and-elements.lesson>Parabola definition, canonical equation, characteristic points and elements</A>  at this site).


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

Hence, receiver should be placed on the parabola axis at the distance of  {{{p/2}}} = {{{90/2}}} = 45 feet from the vertex.
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Solved, explained and completed.


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On parabolas, see the lessons 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Parabola-definition--canonical-equation--characteristic-points-and-elements.lesson>Parabola definition, canonical equation, characteristic points and elements</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Parabola-focal-property.lesson>Parabola focal property</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Tangent-lines-to-a-parabola.lesson>Tangent lines and normal vectors to a parabola</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Optical-property-of-a-parabola.lesson>Optical property of a parabola</A>


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Practical-problems-from-the-archive-related-to-ellipses-and-parabolas.lesson>Practical problems from the archive related to ellipses and parabolas</A> 


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/REVIEW-of-lessons-on-parabolas.lesson>OVERVIEW of lessons on parabolas</A>. 

in this site.