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20 May, 07:02

Write the equation for a parabola with a focus at (-8,-1) (?8,?1) left parenthesis, minus, 8, comma, minus, 1, right parenthesis and a directrix at y=-4y=?4y, equals, minus, 4

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  1. 20 May, 08:29
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    This will be a parabola which opens upwards. and with a vertex at ((-8, (-1-1.5) = (-8, - 2.5). (The vertex is halfway between the focus and the directrix).

    The general form is (x-h) ^2 = 4p (y - k) where (h, k) is the vertex.

    So we can write the equation as

    (x + 8) ^2 = 4p (y + 2.5)

    p = 1.5 so we have

    (x + 8) ^2 = 6 (y + 2.5)

    x^2 + 16x + 64 = 6y + 15

    6y = x^2 + 16x + 49

    y = (1/6) x^2 + (8/3) x + (49/6) is the answer
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