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17 July, 20:30

8 PTS! In two or more complete sentences, Explain how you would find the equation of a parabola, given the coordinate of the focus and the equation of the directrix.

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  1. 17 July, 21:38
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    Yah it would a even number or something even i think
  2. 17 July, 23:01
    0
    2 types of parabolas

    left right or up down opening ones

    left right ones are in form (y-k) ²=4p (x-h)

    up down ones are (x-h) ²=4p (y-k)

    in all of them, the vertex is (h, k)

    p is the distance from the vertex to the focus, also the shortest distance from the vertex to the directix making p half of the distance of the shortest path from focus to directix

    if p is positive, then the parabola opens up or right

    if p is negative then the parabola opens down or left

    if the directix is y=something, then it is a up down parabola

    if directix is x=something, then it is a left right parabola

    directix is outside the parabola, kind of at the back

    so lets say we had

    focus = (2,3) and directix is x=-4

    dirextix is x = - 4 so left right

    from x=-4 to x=2 (focus), that is distance of 6

    6/2=3

    p=3

    wait, ok, so directix is on oposite side of opening

    hmm, - 4 is to left of the 2 so

    the direxix is at back so the parabola opens to the right

    p=3, positive 3

    then we have the vertex is halfway between those

    so 3 back from focus is from (2,3) to (-1,3)

    so vertex is (-1,3)

    equation is

    (y-3) ²=4 (3) (x - (-1))

    (y-3) ²=4 (3) (x+1)
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