SOLUTION: A satellite dish is shaped like a paraboloid of revolution. The signals that emanate from a satellite strike the surface of the dish and are reflected to a single point, where the

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Question 188514This question is from textbook Precalculus
: A satellite dish is shaped like a paraboloid of revolution. The signals that emanate from a satellite strike the surface of the dish and are reflected to a single point, where the receiver is located. If the dish is 10 feet across at its opening and 4 feet deep at its center, at what position should the receiver be placed? This question is from textbook Precalculus

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
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: (10,4)
Plug it in and solve for 'c':
y = (1/4c)x^2
4 = (1/4c)10^2
4 = (1/4c)100
4 = (1/c)25
4c = 25
c = 25/4
c = 6.25 feet