Question

can someone please help me find and graph the focus and directrix of this equation.

Answer 1

the equation is y = (1/32)x^2. i graphed it with my calculator and drew it on my paper. i don't understand how to find the focus and directrix.

Answer 2

you need the vertex first

Answer 3

how do i find the vertex.

Answer 4

general form for this kind of problem is
\[4p(y-k)=(x-h)^2\] but in your case you have
\[y=\frac{1}{32}x^2\] lets make it look like the top one

Answer 5

multiply both sides by \(32\) and get
\[32y=x^2\] which we can visualize as \(32(y-0)=(x-0)^2\) making the vertex the origin \((0,0)\)

Answer 6

satellite plz come help me when you done

Answer 7

then we have \(4p=32\) so what is \(p\)?

Answer 8

how did you even get 4p = 32 from that? like i literally don't understand.

Answer 9

i know the focus is (0, p) and i guess you're saying p is 8 but i don't know how you managed to get 4p = 32.

Answer 10

i multiplied both sides of
\[y=\frac{1}{32}x^2\] by \(32\) to make it look more like
\[4py=x^2\]

Answer 11

well am i right in saying the focus is 0,8?

Answer 12

this \(4p(y-k)=(x-h)^2\) is the general form of a parabola that opens up or down
the vertex is \((h,k)\) and \(p\) is the distance from the vertex to the focus, and also to the directrix

Answer 13

was that the answer satellite

Answer 14

once we make it look like that , we read off \(4p=32\) and then we know \(p=8\)

Answer 15

so the focus is 0,8 and the directrix is y = -p so the directrix is -8 on the y axis

Answer 16

yes

Answer 17

well not "-8 on the y axis" but rather the line \(y=-8\) which is what i assume you meant

Answer 18

yeah. i understand how to find the focus and directrix but i still don't understand how to find p. like my next one is x = -(1/12)y^2, i know that this is a vertical directrix now instead of a horizontal but i still don't know how to find p. @satellite73