A parabola has a Vertex at (4,-2) and a Focus at (6,-2). Find the equation of the parabola

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  1. math_celebrity

    math_celebrity Administrator Staff Member

    A parabola has a Vertex at (4,-2) and a Focus at (6,-2). Find the equation of the parabola and the lotus rectum.

    Equation of a parabola given the vertex and focus is:
    (xh)^2 = 4p(yk)

    The vertex (h, k) is 4, -2
    The distance is p, and since the y coordinates of -2 are equal, the distance is 6 - 4 = 2.
    So p = 2

    Our parabola equation becomes:
    (x - 4)^2 = 4(2)(y - -2)
    (x - 4)^2 = 8(y + 2)

    Latus rectum of a parabola is 4p, where p is the distance between the vertex and the focus
    LR = 4p
    LR = 4(2)
    LR = 8


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