Question

Find the standard form of the equation of the parabola with a focus at (0, -9) and a directrix y = 9.

Answer 1

Answer Choices:
A. y = -1/9x^2
B. y^2 = -36x
C. y = -1/36x^2
D. y^2 = -9x

Answer 2

What do you think the answer is? Do you know what a focus is?

Answer 3

What's the formula for parabola? How can you plug it into the formula?

Answer 4

The formula is (x−h)^2=4p(y−k)

Answer 5

@tom982
Where (h,k) is the vertex

Answer 6

and focus is either (h, k+p) or (h+p ,k)

Answer 7

That's all I know

Answer 8

Anybody?

Answer 9

Let's work through it with the material you provided.

\[ (x−h)^2=4p(y−k)\]
focus at \( (0, -9)\) and directrix of \(y = 9\)

Any idea where the vertex will be?

Answer 10

I don't know

Answer 11

I don't know how to get the vertex from that information.

Answer 12

yo, @turmoilx2 are you going to take part here?

Answer 13

hmmmmmmmmm.....

Answer 14

Yes. I am replying. @whpalmer4

Answer 15

I just don't see what I'm supposed to do with the information yet.

Answer 16

Do you know the definition of what a parabola is? It is a set of points that satisfy some rule, do you know what the rule is?

Answer 17

sorry, open study is not behaving well for me, going to try restarting my browser, brb...

Answer 18

I'd suggest that you attempt to graph this parabola. Draw a set of axes and locate the given point and the given line.

Identify the point, the line and the vertex of your parabola. Even a quick sketch would be helpful.

Your job will be to relate distances in this drawing to the equation of a parabola. What does "p" in your formula represent? If you're not sure, look it up, please. Try the Internet and search for "equations of a parabola."

Your graph should give you the value of p by inspection.

Answer 19

OS is not behaving well for me either. That is why I haven't been participating in the solving of my question.

Answer 20

Important: The vertex of a parabola lies exactly halfway between the directrix (a line) and the focus (a point).
If the directrix is the horiz. line y=9 and the focus is at (0,-9), what are the coordinates of the vertex? Again, I ask you to graph this situation. Show the directrix, the focus and the vertex.

Answer 21

Here's my sketch

Answer 22

Please see the following on the 'Net:

https://www.google.com/search?sourceid=chrome-psyapi2&ion=1&espv=2&es_th=1&ie=UTF-8&q=directrix%20parabola&oq=directrix%20parabola&aqs=chrome..69i57j0l5.3199j0j7

The very first illustration shows that the vertex is halfway between the directrix and the focus. p is the distance between the focus and the vertex. What is p here?

Answer 23

Will YOUR parabola open up or down? You are given the directrix: y=9, and the focus: (0,-9). The vertex is in between. UP or DOWN?