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4 September, 02:47

Find the focus and directrix of parabola xsquared = 2y

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  1. 4 September, 03:35
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    directrix: y = - 1/2; focus = (0,1/2)

    Step-by-step explanation:

    rewrite in standard form:

    2y = x^2

    factor 4

    4 * (y/2) = x^2

    rewrite as

    4 * 1/2 (y - 0) = (x - 0) ^2

    therefore

    (h, k) = (0,0), p = 1/2

    directrix is line || to x-axis, distance - p from the center (0,0) y-coordinate (of the parabola)

    y = 0 - p

    y = 0 - 1/2

    y = - 1/2

    now for the focus!

    the focus is distance p from center (0,0) along y-axis - -> (0, 0+p)

    therefore

    (0,0+1/2)

    (0,1/2) is the focus!
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