SOLUTION: A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by rotating a parabola around its axis of symmetry. The receiver is to be located at th

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by rotating a parabola around its axis of symmetry. The receiver is to be located at th      Log On


   

Question 1114351: A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by rotating a parabola around its axis of symmetry. The receiver is to be located at the focus. If the dish is 36 feet across at its opening and 3 feet deep at its center, where should the receiver be placed?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Vertex as the origin, concave upward.
y=ax%5E2


Two points other than (0,0) are (-18,3) and (18,3), unit being feet.


a=y%2Fx%5E2
a=3%2F%2818%5E2%29
a=3%2F%283%2A6%2A18%29
a=1%2F%286%2A18%29
-
y=%281%2F108%29x%5E2
OR equivalently
highlight_green%28108y=x%5E2%29


Let p be distance above the vertex to put the receiver (placement of the focus).

4p=108
p=108%2F4
highlight%28p=27%29