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anonymous

  • one year ago

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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  1. anonymous
    • one year ago
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    @ganeshie8

  2. anonymous
    • one year ago
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    @UsukiDoll

  3. anonymous
    • one year ago
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    @Astrophysics

  4. anonymous
    • one year ago
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    i know how to do it when they give me x but they gave my y instead

  5. Astrophysics
    • one year ago
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    |dw:1435907166360:dw| ok first lets just plug what we have, then we will see what formula to use.

  6. Astrophysics
    • one year ago
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    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?

  7. anonymous
    • one year ago
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    yea

  8. anonymous
    • one year ago
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    we can plug in h k and y

  9. anonymous
    • one year ago
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    but not x and p

  10. Astrophysics
    • one year ago
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    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.

  11. anonymous
    • one year ago
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    x = h - p

  12. Astrophysics
    • one year ago
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    Well, let me ask you a question, what way is the parabola, is it opening up, down, left, right what's going on?

  13. Astrophysics
    • one year ago
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    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.

  14. Astrophysics
    • one year ago
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    |dw:1435908052023:dw| right?

  15. anonymous
    • one year ago
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    so the directrix would be 0?

  16. Astrophysics
    • one year ago
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    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)

  17. anonymous
    • one year ago
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    ohhhh ok

  18. Astrophysics
    • one year ago
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    Ok cool, so our graph looks something like this |dw:1435908205110:dw| now we can write the equation

  19. Astrophysics
    • one year ago
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    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!

  20. Astrophysics
    • one year ago
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    |dw:1435908337698:dw|

  21. anonymous
    • one year ago
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    so p would be 10?

  22. Astrophysics
    • one year ago
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    Nope, not 10, but 9, sorry about the picture, I just put 10 there to give an idea of the scale.

  23. anonymous
    • one year ago
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    oh ok yea i see the 9 now

  24. Astrophysics
    • one year ago
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    Alright cool, now just plug in all the value and standard form is in the following: \[x=ay^2+by+c\]

  25. anonymous
    • one year ago
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    but in the answer choice the closest thing to 9 for p is -9, would -9 be right?

  26. Astrophysics
    • one year ago
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    Yup, -9 is good

  27. anonymous
    • one year ago
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    oh wait isnt it 1/4p?

  28. anonymous
    • one year ago
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    y^2= 1/4px

  29. Astrophysics
    • one year ago
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    May I see your answer choices actually

  30. anonymous
    • one year ago
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    y = -1/9x^2 y2 = -36x y = -1/36x y2 = -9x

  31. anonymous
    • one year ago
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    wouldnt it be c

  32. Astrophysics
    • one year ago
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    Ok I see so it wants it in \[y = \frac{ 1 }{ 4 p}(x-h)^2+k\] form

  33. Astrophysics
    • one year ago
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    That looks good to me

  34. anonymous
    • one year ago
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    ok thank you! could you help me with one more but ill make a new post so i can give u another medal

  35. Astrophysics
    • one year ago
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    That should be x^2 though

  36. Astrophysics
    • one year ago
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    y=-1/36x^2

  37. anonymous
    • one year ago
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    yea its x^2 i forgot to put the ^2

  38. Astrophysics
    • one year ago
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    Ok :)

  39. Astrophysics
    • one year ago
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    \[y = -\frac{ 1 }{ 36 }x^2\] so just in case, that is your final answer

  40. anonymous
    • one year ago
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    ok thank you

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