SOLUTION: A satelite dish has a shape called a paraboloid, where each cross section is a parabola. Since radio signals (parallel to the axis) will bounce off the surface of the dish to the f

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: A satelite dish has a shape called a paraboloid, where each cross section is a parabola. Since radio signals (parallel to the axis) will bounce off the surface of the dish to the f      Log On


   

Question 1119578: A satelite dish has a shape called a paraboloid, where each cross section is a parabola. Since radio signals (parallel to the axis) will bounce off the surface of the dish to the focus, the receiver be placed at the focus. How far should the receiver be from the vertex, if the dish is 10 ft across, and 4 ft deep ? Round o your answer to 2 decimal places.

thank youuu
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Put the parabola cross section description onto a cartesian plane system with vertex at origin and expect focus to be above the vertex. You know three points.
(0,0), (5,4), and (-5,4).

y=ax%5E2

a=y%2Fx%5E2
a=4%2F%285%2A5%29
a=4%2F25
-
y=%284%2F25%29x%5E2
%2825%2F4%29y=x%5E2
If p is how far focus is from vertex, then 4p=25%2F4
p=25%2F16.

Receiver should be 25%2F16 feet or 1 foot 6 inches and 3%2F4 inch from the vertex.