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18 December, 00:19

Find the equation of a parabola with focus (2, - 3) and directrix x = 5.

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  1. 18 December, 02:55
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    Yay

    directix x=5

    that means the parabola opens left or right

    the equation is

    (y-h) ²=4p (x-h)

    alrighty

    vertex is (h, k)

    p is distance from focus to vertex

    also distance from vertex to directix

    if p>0 then the parabola opens to the right and focus is to the right of directix

    if p<0 then the parabola opens to the left and focus is to the left of directix

    alrighty

    the distance between directix and focus divided by 2=p

    hmm, note which one is to the left or right of which

    directix is x=5

    focus is (2,-3) where x=2

    focus is to the left of directix

    alrighty

    fro m 5 to 2 the distance is 3

    3/2=1.5

    and since the focus is to the left of the directix, it is - 1.5

    so the parabols opens to the left

    the vertex is 1.5 untis to the right of the focus

    so vertex is at (3.5,-3)

    so

    equation is

    (y - (-3)) ²=4 (-1.5) (x-3.5)

    (y+3) ²=4 (-1.5) (x-3.5)
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