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Thread: parabolic tv antenna ( HELP!!! )

  1. #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. #2
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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 $\displaystyle (-9,8)$ , $\displaystyle (0,0)$ , and $\displaystyle (9,8)$ are on the parabola.

    $\displaystyle y = kx^2$

    $\displaystyle 8 = k(9)^2$

    $\displaystyle k = \frac{8}{81}$

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

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

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

    equating ...

    $\displaystyle 4p = \frac{81}{8}$

    $\displaystyle p = \frac{81}{32}$

    find the focal point.
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