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Math Help - directrix of y=-4

  1. #1
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    directrix of y=-4

    have a vertex at (-4,-1) with a vertical axis of symennetry. which one has a directrix of y=-4

    so far i got (x+4)^2=?(y+1)

    what is the ?..?!! how do i get that
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  2. #2
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    Directrix of a parabola

    Hello peekybooyou
    Quote Originally Posted by peekybooyou View Post
    have a vertex at (-4,-1) with a vertical axis of symennetry. which one has a directrix of y=-4

    so far i got (x+4)^2=?(y+1)

    what is the ?..?!! how do i get that
    You're right so far. You have used the fact that the parabola X^2 = 4aY has vertex at (0,0) and a vertical axis of symmetry. You've replaced X by (x+4) and Y by (y+1) to give a parabola whose vertex is at (-4,-1).

    Now you need to use the fact that the parabola X^2 = 4aY has directrix Y = -a.

    If in the (x,y) coordinates, the directrix is y = -4, in the (X,Y) coordinates it is

    Y = y+1 =-3

    \Rightarrow a = 3

    So in (X,Y) coordinates the equation is X^2 = 12 Y; in (x,y) coordinates it is (x+4)^2 = 12(y+1)

    Grandad
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