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

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 $x=\frac{d}{2}=\frac{10 ft}{2}=5 ft$

$y=2 ft$ is the depth

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

Finding $p$:

$p=\frac{x^{2}}{4y}$

$p=\frac{(5 ft)^{2}}{4(2 ft)}$

Finally:

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