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16 January, 18:53

Derive the equation of the parabola with a focus at (6, 2) and a directrix of y = 1.

f (x) = - 1/2 times (x - 6) ^2 + 3/2

f (x) = 1/2 times (x - 6) ^2 + 3/2

f (x) = - 1/2 times (x + 3/2) ^2 + 6

f (x) = 1/2 times (x + 3/2) ^2 + 6

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  1. 16 January, 22:08
    0
    (x-h) ^2=4p (y-k)

    we know it is this one because the directix is y=something and not x=something

    (h, k) is the vertex

    p is the distance from the vertex to the focus

    it is 1/2 the distance from the vertex to the directix

    if p is positive, the focus is above the vertex

    if p is negative, the focus is below the vertex

    we have

    focus is (6,2) and directix is y=1

    distance from (6,2) to y=1 is the distance from 2 to 1 which is 1

    1/2=p

    since 1<2, we see that the focus is above the vertex (when the focus is greater than the directix, then the graph opens to the right or up)

    p=1/2

    1/2 below (6,2) is (6,1.5)

    vertex is (6,1.5)

    p=1/2

    (x-6) ^2=4 (0.5) (y-1.5)

    (x-6) ^2=2 (y-1.5)

    (x-6) ^2=2y-3

    2y = (x-6) ^2+3

    divide both sides by 2

    y=1/2 times (x-6) ^2+3/2

    f (x) = 1/2 times (x-6) ^2+3/2

    2nd option is answer
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