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Math Help - Find equation of the parabola

  1. #1
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    Find equation of the parabola

    If the vertex is on the line x=2; axis parallel to x axis, Latus rectum = 6 and passing through (8,2)

    Help please. No idea. The axis parallel to x axis made it confusing.
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  2. #2
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    Quote Originally Posted by reiward View Post
    If the vertex is on the line x=2; axis parallel to x axis, Latus rectum = 6 and passing through (8,2)

    Help please. No idea. The axis parallel to x axis made it confusing.
    1. Since the point P(8, 2) lies at the right side of the vertex the parabola opens to the right. The general equation of such a parabola is

    (y-h)^2=4p(x-k) with the vertex at V(k, h)

    2. You already know that the latus rectum l = 4p which is 6 in your question.

    3. You know the x-coordiante of the vertex (k = 2) and you know the coordinates of one point of the parabola. Plug in all known values:

    (y-h)^2=6(x-2)

    Solve for h.


    EDIT: There are two parabolas which satisfy the given conditions!
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