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Help With tricky math word problem?

A satellite is shaped like a paraboloid of revolution. the Signals that emanate from the satellite 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 the opening and 4 feet deep at its center, at what position should the receiver be placed

1 Answer

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  • 8 years ago

    the vertex of the parabola is (0,-4) and the roots (zeros) are plus and minus 7

    a(x^2 - 49) = 0

    y = a(x - 0)^2 - 4

    ax^2 - 49a = ax^2 - 4 ___ a = 4/49

    the focal length (distance from vertex to focus) is ___ 1 / 4a

    ___ in this case ___ 49 / 16

    so the receiver should be in the middle of the opening

    ___ 49/16 feet from the bottom ___ 3 feet 3/4 inch

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