Question

A satellite dish is in the shape of a parabolic surface. Signals coming from a satellite strike the surface of the dish and are reflected to the​ focus, where the receiver is located. The satellite dish has a diameter of 10 feet and a depth of 2 feet. How far from the base of the dish should the receiver be​ placed?

Answer 1

Answer: 3.125 ft

Step-by-step explanation:

If this dish has the form of a concave upward parabola and its vertex
`p` is at the origin, its corresponding equation is:

`x^(2)=4py`

Where:

`x` is the radius, which can be found by dividing the diameter
`d=10 ft` by half. Hence
`x=(d)/(2)=(10 ft)/(2)=5 ft`

`y=2 ft` is the depth

`p` is the vertex of the parabola, where its base is

Finding
`p`:

`p=(x^(2))/(4y)`

`p=((5 ft)^(2))/(4(2 ft))`

Finally:

`p=3.125 ft` This is where the the receiver should be placed