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Thread: parabolic tv antenna ( HELP!!! )

  1. May 18th 2010, 03:48 PM #1
    ddo
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    parabolic tv antenna ( HELP!!! )

    a parabolic tv antenna is 18 feet across and 8 feet deep if the receiver is placed at the focus how far is it from the vertex?
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  2. May 18th 2010, 04:46 PM #2
    skeeter
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    Quote Originally Posted by ddo View Post
    a parabolic tv antenna is 18 feet across and 8 feet deep if the receiver is placed at the focus how far is it from the vertex?
    let the vertex be at the origin.

    the points (-9,8) , (0,0) , and (9,8) are on the parabola.

    y = kx^2

    8 = k(9)^2

    k = \frac{8}{81}

    y = \frac{8}{81} x^2

    general parabola equation w/ vertex at the origin ...

    y = \frac{x^2}{4p}

    equating ...

    4p = \frac{81}{8}

    p = \frac{81}{32}

    find the focal point.
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