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

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

Mathematics
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i know how to do it when they give me x but they gave my y instead
|dw:1435907166360:dw| ok first lets just plug what we have, then we will see what formula to use.
The graph is sort of bad, but we can fix that after. We will have to use the equation \[(x-h)^2=4p(y-k)\] look familiar, so far so good?
yea
we can plug in h k and y
but not x and p
Ok so lets just write out what we have so far, h = 0 k = -9 Any idea what p might be? This is a bit tricky.
x = h - p
Well, let me ask you a question, what way is the parabola, is it opening up, down, left, right what's going on?
Also, we can figure out the vertex right away, as it's the same distance from vertex to directrix and vertex to focus. So it's the middle point between the focus and directrix.
|dw:1435908052023:dw| right?
so the directrix would be 0?
No no, we're given the directrix, it's y = 9, but the vertex is (0,0) as it's the middle point between the directrix and the focus, where we were given the focus (0,-9)
ohhhh ok
Ok cool, so our graph looks something like this |dw:1435908205110:dw| now we can write the equation
Because it cannot cross the directrix, so if it was the other way, this would happen |dw:1435908273394:dw| and it can't cross the directrix!
|dw:1435908337698:dw|
so p would be 10?
Nope, not 10, but 9, sorry about the picture, I just put 10 there to give an idea of the scale.
oh ok yea i see the 9 now
Alright cool, now just plug in all the value and standard form is in the following: \[x=ay^2+by+c\]
but in the answer choice the closest thing to 9 for p is -9, would -9 be right?
Yup, -9 is good
oh wait isnt it 1/4p?
y^2= 1/4px
May I see your answer choices actually
y = -1/9x^2 y2 = -36x y = -1/36x y2 = -9x
wouldnt it be c
Ok I see so it wants it in \[y = \frac{ 1 }{ 4 p}(x-h)^2+k\] form
That looks good to me
ok thank you! could you help me with one more but ill make a new post so i can give u another medal
That should be x^2 though
y=-1/36x^2
yea its x^2 i forgot to put the ^2
Ok :)
\[y = -\frac{ 1 }{ 36 }x^2\] so just in case, that is your final answer
ok thank you

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