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2 July, 14:29

What is the equation of a parabola with (-1, - 3) as its focus and y = 1 as its directrix? Enter the equation in the box.

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  1. 2 July, 17:38
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    The answer

    the general formula showing parabola is

    y = ax² + bx + c, its standard form is y = a (x-h) ² + k

    the focus formula is

    F (h, k + 1 / 4a) and the directrix is

    the directrix is V (k - 1/4a)

    so he equation of a parabola with (-1, - 3) as its focus implies

    (h, k + 1 / 4a) = (-1, - 3)

    h = - 1, and k + 1 / 4a = - 3

    the directrix is k - 1/4a = 1

    we should solve the system of equation

    k + 1 / 4a = - 3

    k - 1/4a = 1

    2k = - 3+1 = - 2, so k = - 1 and when we use this value

    -1 - 1/4a = 1 implies 2 = - 1/4a this equation give a = - 1/8

    finally the equation is

    y = - 1/8 (x + 1) ² - 1
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