Question

Find the standard form of the equation of the parabola with a focus at (0, -8) and a directrix at y = 8.

Answer 1

HI!!

Answer 2

this is real real easy if you know what it looks like
do you know that?

Answer 3

\[y=a(x-h)^2+k\]

Answer 4

i was asking if you knew what the parabola looked like, not the form of it, but rather the picture of it

Answer 5

@satellite73 drew the directrix and the focus
do you know how the parabola looks? i.e. opens up, down, left or right? also the vertex?

Answer 6

if so, we can answer this question in like 2 seconds
if not, it is almost impossible

Answer 7

vertex would be (0,0) right?

Answer 8

yes

Answer 9

does it open up or down?

Answer 10

up?

Answer 11

hmm no

Answer 12

oh sorry down, i mixed up the a>0 and a<0

Answer 13

it opens down because the focus is below the directrix

Answer 14

that means it is going to look like
\[-4p(y-k)=(x-h)^2\] but since \((h,k)=(0,0)\) it is just
\[-4py=x^2\]

Answer 15

\(p\) is the distance between the focus and the vertex, which is evidently 8

Answer 16

so
\[-4\times 8y=x^2\] or
\[-32y=x^2\] and we are done

Answer 17

the only answer i have that is similar to that is y^2= -32x

Answer 18

that is why it is important to know what it looks like first, so you know the right form to put it in

Answer 19

is it the same?

Answer 20

is one choice
\[y=-\frac{1}{32}x^2\]

Answer 21

yes

Answer 22

no they are not the same, but
\[-32y=x^2\] is the same as
\[y=-\frac{1}{32}x^2\]

Answer 23

okay thank you very much!

Answer 24

i.e. divide both sides by \(-32\)

Answer 25

\[\color\magenta\heartsuit\]

Answer 26

is there a way you could help me on a few other questions?

Answer 27

if i know how
go ahead and post one

Answer 28

you can post it here if you like