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Math Help - How to find coordinates of the focus and the equation of the directrix of the parabol

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    Question How to find coordinates of the focus and the equation of the directrix of the parabol

    Hi I have an exercise and Iíve been struggling for a while with that. This is it:

    Find coordinates of the focus and the equation of the directrix of the parabola whose equations is:

    3y"squer"=8x
    The chord which passes through the focus parallel to the directix is called the latus rectum of the parabola. Shown that the latus rectum of the above parabola has length8/3.

    I do not understand this exercise at all. I have always thoughts that parabola equation looks like that:
    y = 4x"squer" -4x +3
    Anyone know how to resolve this problem?
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    Re: How to find coordinates of the focus and the equation of the directrix of the par

    Quote Originally Posted by leketapis View Post
    Hi I have an exercise and Iíve been struggling for a while with that. This is it:

    Find coordinates of the focus and the equation of the directrix of the parabola whose equations is:

    3y"squer"=8x
    The chord which passes through the focus parallel to the directix is called the latus rectum of the parabola. Shown that the latus rectum of the above parabola has length8/3.

    I do not understand this exercise at all. I have always thoughts that parabola equation looks like that:
    y = 4x"squer" -4x +3
    Anyone know how to resolve this problem?
    3y^2 = 8x

    y^2 = \frac{8x}{3}

    this is a parabola with the x-axis as the axis of symmetry. the parabola opens to the right.

    your text should have this form for a parabolic equation ...

    (y-k)^2 = 4p(x-h)^2 , where (h,k) are the coordinates of the vertex, (h+p,k) are the coordinates of the focus, and x = h-p is the directrix.

    (y-0)^2 = \frac{8}{3}(x - 0)^2

    vertex is at (0,0)

    4p = \frac{8}{3}

    p = \frac{2}{3}

    \left(\frac{2}{3} , 0\right) is the focus

    x = -\frac{2}{3} is the directrix


    here is a link for you to investigate further ...

    Conics: Parabolas: Introduction
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