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Math Help - coordinate geometry about parabolas

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    coordinate geometry about parabolas

    A chord of the parabola that is perpendicular to the axis and 1 unit from the vertex has a length of 1 unit. How far is the vertex from the focus?

    ***by the way, the answer to this problem is 1/16. I just want to know how did you get the right answer to this problem. thanks!!
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    Quote Originally Posted by fishlord40 View Post
    A chord of the parabola that is perpendicular to the axis and 1 unit from the vertex has a length of 1 unit. How far is the vertex from the focus?

    ***by the way, the answer to this problem is 1/16. I just want to know how did you get the right answer to this problem. thanks!!
    1. Let the equation of the parabola be

    4py = x^2

    where p is the distance of the focus from the vertex.

    2. You know the coordinates of 2 points of the parabola: P(-\tfrac12, 1), Q(\tfrac12, 1)

    3. Plug in the coordinates of Q into the equation of the parabola and solve for p:

    4p \cdot 1 = \left(\frac12\right)^2
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