Question

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

\(-\dfrac 1{40}x^2 = y\)

Answer 1

I know the vertex is 0, 0
and I know that something is -10, but i'm not sure if it is the focus or directrix

Answer 2

First remember that focus is a "point" and directrix is a "line"

Answer 3

Okay, so it would be the focus that is 0, -10?

Answer 4

Yes focus is (0, -10)

Answer 5

yay! how would I go about finding the directrix and focal width?

Answer 6

directrix is \(y = -(-10)\)
which is same as \(y = 10\)

Answer 7

and the focal width is 40?

Answer 8

Yep!

Answer 9

:D
Thanks!

Answer 10

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Answer 11

wow!