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Thread: 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 $\displaystyle X^2 = 4aY$ has vertex at $\displaystyle (0,0)$ and a vertical axis of symmetry. You've replaced $\displaystyle X$ by $\displaystyle (x+4)$ and $\displaystyle Y$ by $\displaystyle (y+1)$ to give a parabola whose vertex is at $\displaystyle (-4,-1)$.

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

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

    $\displaystyle Y = y+1 =-3$

    $\displaystyle \Rightarrow a = 3$

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

    Grandad
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