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23 September, 18:52

what is the equation of the quadratic graph with a focus of (-1,4) and a directrix of y=2? hint: y=a (x-h) ^2+k, a=1/4p

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  1. 23 September, 21:51
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    y = 1/4 (x + 1) ^2 + 3.

    Step-by-step explanation:

    The general form is (x - h) ^2 = 4p (y - k) where the focus is (h, k+p) and the directrix is y = k-p

    So we have h = - 1

    k + p = 4

    k - p = 2 Adding:

    2k = 6 so k = 3 and p = 1.

    Therefore:

    (x + 1) ^2 = 4 (y - 3)

    4y = (x + 1) ^2 + 12

    y = 1/4 (x + 1) ^2 + 3.
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