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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- Apr 19th 2009, 04:55 PMpeekybooyoudirectrix 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 - Apr 19th 2009, 10:51 PMGrandadDirectrix of a parabola
Hello peekybooyouYou'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