11.2.65 A satellite dish is shaped like a paraboloid of revolution. The signals

Question

11.2.65 A satellite dish is shaped like a paraboloid of revolution. The signals that emanate from a satelite strike the surface of the dish and are reflected to a single point, where the receiver is located If the dish is 14 feet across at its opening and 5 feet deep at its center, at what position should the receiver be placed? The receiver should be placed feet from' the base of the dish, along its axis of symmetry (Type an exact answer in simplified form.) Question Help Enter your answer in the answer box and then click Check Answer

Explanation / Answer

You are trying to find 'c' -- the distance between the vertex and the focus.
Think of the equation for a vertical parabola:
y = (1/4c)(x-h)^2 + k
If we place our parabola at the center our equation becomes:
y = (1/4c)x^2
.
The problem gives you a point on the parabola: (14, 5)
Plug it in and solve for 'c':
y = (1/4c)x^2

5 = (1/4c)14^2

5 = (1/4c)196
5 = (1/c)49
5c = 49
c = 49/5
c = 9.8 feet

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