Question

A satellite dish is in the shape of a parabolic surface. Signals coming from a satellite strike the surface for the dish and are reflected to the focus, where the receiver is located. The satellite dish has a diameter of 14 feet and a depth of 3 feet. How far from the base of the dish should the receiver be placed? Round your answer to the nearest tenth.

Answer 1

Given that we know the base of the parabola is at the origin, and that it is symetrical about the y-axis, we can simplify the equation to

y=ax2=14px2" role="presentation">y=ax2=14px2y=ax2=14px2

which corresponds to the given equation a=14p" role="presentation">a=14pa=14p given above.

Since y=6" role="presentation">y=6y=6 when x=2" role="presentation">x=2x=2,

6=a(2)2=4a" role="presentation">6=a(2)2=4a6=a(2)2=4a

and

a=32" role="presentation">a=32a=32

Thus we have

32=14p12p=2p=16" role="presentation">32=14p12p=2p=1632=14p12p=2p=16

So, the receiver should be placed 16" role="presentation">1616 of a foot, or 2 inches, above the base.