Question

Parabola help?

Answer 1

Find the vertex, focus, directrix, and focal width of the parabola.
\[-1/40x^2=y\]
negative 1 divided by 40 x squared equals y

Answer 2

I know the vertex is (0,0) but can someone refresh me on how to solve for the other things.

Answer 3

would be easier to see if you multiply by \(-40\) and start with \[-40y=x^2\]

Answer 4

which looks a lot like \[4py=x^2\] you can sort of see the \(p\) instantly

Answer 5

The equation I was given to use was (x-h)^2 = 4p(y-k) and then y = k-p

Answer 6

in your equation \(h=k=0\) so it really does look like that , just \[x^2=-40y\]

Answer 7

open up or down?

Answer 8

Would it be down since p < 0

Answer 9

yes it would

Answer 10

what is \(p\) exactly ?

Answer 11

Is it -40

Answer 12

no, \(-40=4p\)

Answer 13

-10?

Answer 14

yes

Answer 15

so the focus is 10 units down from \((0,0)\) and the directrix is the horizontal line 10 units up

Answer 16

Okay that makes sense. How do I find the focal width?

Answer 17

idk
it might be just the the absolute value of p
we can google it

Answer 18

no i was wrong, it is not p it is \(|4p|\)

Answer 19

I believe it has something to do with 4(p)

Answer 20

So that would make it 160?