SOLUTION: a satellite dish has a shape called paraboloid where each cross section is a parabola since ratio signals (parallel to the x-axis will bounce off the surface of the dish to the foc

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: a satellite dish has a shape called paraboloid where each cross section is a parabola since ratio signals (parallel to the x-axis will bounce off the surface of the dish to the foc      Log On


   

Question 1092181: a satellite dish has a shape called paraboloid where each cross section is a parabola since ratio signals (parallel to the x-axis will bounce off the surface of the dish to the focus the receiver should be placed at the focus.How far should the receiver be from the vertex if the dish is 12 ft across and 4.5 ft deep at the vertex?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

Assuming an upward opening parabola with its vertex at the origin, the vertex form of the equation of a parabola that I like to use is

y+=+%281%2F%284p%29%29x%5E2

With that form of the equation, the parameter p is the distance from the vertex to the focus and the distance from the vertex to the directrix.

We can use the given information to find the value of p and thus determine how far from the vertex the receiver should be.

If we picture the parabola as opening upward with its vertex at the origin, then the outermost points on the dish are at the points (6,4.5) and (6,-4.5). So

4.5+=+%281%2F%284p%29%29%286%5E2%29
9%2F2+=+9%2Fp
p=2

So the receiver should be placed 2 feet from the vertex.