How do you find the directrix of a parabola? Like if you had y=x^2/32? Thanks!

Question

mimi_x3 · Answer

$$ y = \frac{x^2}{32} => 32y = x^2 => x^2 = 32y$$

mimi_x3 · Answer

looks like you have to find the vertex first; then the directrix..

lgbasallote · Answer

^genius

anonymous · Answer

It told me to find the equation, which is what I thought the y=x^2/32 was. Because it is supposed to be y=? I don't think I phrased my first question right..

mimi_x3 · Answer

a parabola is: $(x-h)^2 = 4A(y-k)$

mimi_x3 · Answer

What is exactly the question?

anonymous · Answer

Find the equation of the directrix of the parabola y=x^2/32

anonymous · Answer

Then it says the equation is y=__blank__

mimi_x3 · Answer

Ok, are you able to find the vertex or the focal length?

anonymous · Answer

I honestly don't know what that means... Like I know what the vertex is, but focal length goes over my head.

mimi_x3 · Answer

Tell what is the vertex for your question?

mimi_x3 · Answer

tell me*

anonymous · Answer

Honestly, I don't know.. Um. I know what it is, but I don't really know how to find it. Super embarrassing & I'm super sorry.. I'm not very good at math.. but I know one of the equations you need to use is like (1/4)px^2 or something

mimi_x3 · Answer

okay agree that parabola is $x^2  = 4ay$ ?

anonymous · Answer

Sure. :)

mimi_x3 · Answer

and when the parabola is like that the vertex is $0,0$agree?

anonymous · Answer

Yes

mimi_x3 · Answer

$V(0,0)$

mimi_x3 · Answer

then the focus is $(0,a)$

anonymous · Answer

Okay, but this is equation isn't in that form so we don't know exactly what a is, right?

mimi_x3 · Answer

your equation is $x^2=32y$

anonymous · Answer

Wait, a=8

mimi_x3 · Answer

yes!

anonymous · Answer

So the focal point thing is (0,8) right?

mimi_x3 · Answer

that is the focus, the focal length is 8. now what about the directrix? the directrix is $y=-a$

anonymous · Answer

so y=-8.

mimi_x3 · Answer

yess!

anonymous · Answer

So what equation do we put that into? into the x^2=ay?

mimi_x3 · Answer

that is just the question of  parabola. which is similar to your equation. that is why you used it to find the focal length.
you have already finished the question; you aready found the directrix

anonymous · Answer

But I thought I had to find the equation? Like the equation for the directrix?

mimi_x3 · Answer

the equation of the directrix is $y=-a$ and you just found it $y=-8$
what else do you want to find?

anonymous · Answer

Oh. Silly me! Nothing, I just didn't realize it was that simple..

mimi_x3 · Answer

well it is not that hard :)

anonymous · Answer

Haha, I guess not ! & Thanks for your help! :) Really appreciate it!