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Math Help - Find equation of the parabola

  1. #1
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    Find equation of the parabola

    If the axis is parallel to x axis, Latus Rectum = 1 and passing through (3,1) and (-5,5)

    Help please. No idea. The axis parallel to x axis made it confusing.
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  2. #2
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    Hello reiward
    Quote Originally Posted by reiward View Post
    If the axis is parallel to x axis, Latus Rectum = 1 and passing through (3,1) and (-5,5)

    Help please. No idea. The axis parallel to x axis made it confusing.
    The 'standard' parabola with axis parallel to the x-axis has equation
    y^2 = 4ax
    and if we move the vertex from the origin to the point (h,k), this equation becomes:
    (y-k)^2 = 4a(x-h)
    Now the latus rectum has length 4a. So here 4a = 1, and the equation now becomes:
    (y-k)^2 = (x-h)
    Plug in the values of x and y at the two points you're given:
    \left\{\begin{array}{l}<br />
(1-k)^2=3-h\\<br />
(5-k)^2=-5-h\\<br />
\end{array}\right.

    \Rightarrow\left\{\begin{array}{l}<br />
k=4\\<br />
h=-6\\<br />
\end{array}\right.
    So the equation is:
    (y-4)^2 = x+6
    which can be re-written as:
    x=y^2-8y+10
    if you like.

    Grandad
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