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Find the equation of the parabola with the vertex at the origin and directrix y =5

  • mathematics -

    The vertex is mid-way between the directrix and focal point:

    D(0,5)

    V(0,0)

    F(0,y)


    FV = VD = 1/4a = 5,
    0 - y = 5,
    Y = -5.

    1/4a = 5,
    Multiply both sides by 4a:
    20a = 1,
    a = 1/20.

    Vertex Form: Y = a(x-h)^2 + k,
    Y = 1/20(x-0)^2 + 0,
    Eq: Y =(1/20)x^2

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