precalculas help word problem?

Question

a satellite dish is shaped like a paraboloid of revolution. the signals that emanate form a sattelite strike the surface of the dish and are reflected to a single point, where the receive is located.if the dish is 16 feet across at its opening and 5 feet deep at its center, at what position should the receiver be placed.

Brian · Accepted Answer

Look first at a mid-cross-section of the dish. With the bottom of the dish being the
vertex we have the parabola y = (1/(4p))*x^2 where p is the focal length, which is
where we need to place the receiver.

Since the dish is 16 feet across with a depth of 5 feet, we have that the points 
(-8,5) and (8,5) lie on the parabola.

Thus 5 = (1/(4p))*(8)^2  ---->  4p = 64/5  ----->  p = 16/5 = 3.2.

So we need to place the receiver 3.2 feet directly above the bottom of the dish.

Pi R Squared · Answer

Hi,

Points (-8,0), (0.-5), and (8.0) are points on the parabola y = 5/64xÂ² - 5, and the vertex is at (0,-5).

a = 5/64

Since a = 1/(4p). then:

 5 . . . 1
---- = ----
64 . . 4p

 20p = 64

 p = 16/5 = 3 1/5

 The focus point should be 3 1/5 feet above the vertex. <==ANSWER

 I hope that helps!! :-)

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precalculas help word problem?

2 Answers