Question

Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, 9). I need help

Answer 1

@jhonyy9

Answer 2

y=a(x-h)^+k (h,k) is the vertex

Answer 3

since the vertex is at the origin, it is (0,0)

Answer 4

wait so what am I suppose to do?

Answer 5

@abb0t @jhonyy9 @koymoi

Answer 6

so the vertex is at the origin, and the focus is at (0, 9)
what's the distance from the vertex to the focus?

Answer 7

9 right/

Answer 8

@jdoe0001

Answer 9

right so, notice for the focus to the origin, the "x" coordinate didn't change, the "y" did
that means is a parabola moving upwards
so the "focus form" of a parabola like so is \(\bf (x-h)^2=4p(y-k)\)

(h, k) as the vertex
p = distance from the vertex to the focus
p > 0, opens upward
p < 0, opens downward

Answer 10

ok that makes a little sense

Answer 11

so am I suppose to use that formula? how do I know what to plug in?

Answer 12

well, your vertex is at the origin, and your focal distance is 9

Answer 13

I'm not sure how doing that formula will give me one of my answer options, they seem like they don't match

Answer 14

origin (0,0)

Answer 15

0+p=9

Answer 16

now plug them in ;)

Answer 17

what is p suppose to be?

Answer 18

(h, k) as the vertex
p = distance from the vertex to the focus
p > 0, opens upward
p < 0, opens downward

Answer 19

so p is 9

Answer 20

yes

Answer 21

so what's the next step after finding p?

Answer 22

plug the values in \(\bf (x-h)^2=4p(y-k)\)

Answer 23

actually if you know the vertex is at its origin, the formula could just be x^=4py or y^=4px

Answer 24

then like jdoe said you have to decide which one to use based on the value of p

Answer 25

I am seriously so confused

Answer 26

so x^=4py you know p=9

Answer 27

I am just suppose to have an answer in terms of y or y^2 apparently

Answer 28

plug it in you get x^=36y

Answer 29

after that what do I do? I mean my answer options are
y = 1/36x2

y = 1/9x^2

y^2 = 9x

y^2 = 36x

Answer 30

what did you get for the equation?

Answer 31

for the main one from earlier?

Answer 32

@jdoe0001

Answer 33

yes