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6. Find the equation of each parabola described below.

a) parabola with vertex (0,0) and the focus (0,7)

b) parabola with focus (-3,0) and directrix x=3

c) parabola with vertex (3,3) and directrix x=-1

d) parabola with focus (-2,-1) and directrix y=5

e) ysquared=-6x translated according to ((x,y) -->(x-2,y+4))

could someone help me with these??

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2 answers

  1. You need to know the following:
    vertex at (h,k)
    if it opens up or down:
    4 a (y-k) = (x-h)^2
    a negative a opens down
    if it opens right or left:
    4 a (x-h) = (y-k)^2
    a negative a opens left
    distance vertex to focus = a
    distance vertex to directrix = a
    ALWAYS SKETCH THEM
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    for example a is vertex (0,0) so h = k = 0 and focus (0,7)
    the sketch shows it with axis along the y axis opening up and distance a = 7
    so
    4 * 7 * y = x^2
    or y = x^2/28

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  2. Note that the vertex is halfway between the focus and the directrix by the way.

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