Question

Find the vertex, focus, directrix, and focal width of the parabola.

-1/20 x ^2 = y

Answer 1

I know what the center is for sure, (0, 0) and that the values of h and k are 0, but idk how I would solve for p in the equation of
(x-h)^2 = 4p(y-k)

Answer 2

Hi!
make it look like that

Answer 3

\[x^2=-20y\]

Answer 4

lol SORRY I meant it was vertex not center:p

Answer 5

so then would the value of p be -5?:)

Answer 6

yes i guess

Answer 7

you know what it looks like?

Answer 8

would the directrix be -1/2?

Answer 9

no

Answer 10

wouldn't the directrix be -10?

Answer 11

the vertex is what you said \((0,0)\) and since it opens down the focus is 5 units below the vertex
that puts it at \((0,-5)\)

Answer 12

nvm 5 right?

Answer 13

then the diretrix is 5 units above, but the directrix is a line, not a number
it is the line \(y=5\)