# directrix of y=-4

• April 19th 2009, 04:55 PM
peekybooyou
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
• April 19th 2009, 10:51 PM
Directrix of a parabola
Hello peekybooyou
Quote:

Originally Posted by peekybooyou
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 $(x+4)^2 = 12(y+1)$