Question

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

x^2 = 12y

Answer 1

you got the vertex from the form right?

Answer 2

\[4p(y-k)=(x-h)^2\] vertex is \((h,k)\)

Answer 3

which in your case is pretty clear i hope, if not let me know

Answer 4

vertex 0, 0 right?

Answer 5

yes

Answer 6

and since \(4p=12\) you get \(p=3\) so the focus should be clear too, assuming you know this faces up

Answer 7

again if not, let me know and i will show you

Answer 8

focus 0, 3

Answer 9

yes

Answer 10

and directrix y = -3?

Answer 11

and how about the directrix?

Answer 12

yes

Answer 13

and the focal width is the easiest, it is \(|4p|\)

Answer 14

which is the width of the parabola at the focus

Answer 15

I have no idea on focal width, they didn't even mention it in the lesson

Answer 16

so focal width is 12?