A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

ckallerid

  • one year ago

I require assisstance! Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = −1. f(x) = −one fourth x2 f(x) = one fourth x2 f(x) = −4x2 f(x) = 4x2

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    What is the directrix? How can we use this to help us derive the parabola?

  2. ckallerid
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Honestly I have no clue, Can you give me like a quick run down on how to do any of this?

  3. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The directrix is a special line to the parabola. Consider some point on the parabola, then the distance from the diretrix to this point and the distance from the focus to this point are the same. Mathematically, we can write this as \[ (x-h)^2 + (y-k)^2 = (y-h_1)^2\], where (h,k) is the focus of the parabola and y = h_1 is the equation of the directrix. In this case, h = 0, k = 1, and h_1 = -1.

  4. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Solve for y in this equation and you will get the equation of your parabola.

  5. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you can answer this in like two seconds if you know two things first, what does this look like?

  6. ckallerid
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    a simple plug in problem.

  7. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1443317214435:dw|

  8. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    there is a crude picture with a focus and directrix labelled do you know what the parabola looks like?

  9. ckallerid
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I'm guessing it would look vertical??

  10. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    copy my picture and draw it

  11. ckallerid
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1443317495455:dw|(like I said I have no clue)

  12. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah i can see that

  13. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the vertex is half way between \((0,1)\) and \(y=-1\) like this

  14. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1443317677014:dw|

  15. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the point half way between \((0,1)\) and \(y=-1\) is \((0,0)\) so the vertex is at the origin, and the parabola opens up

  16. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    that means it looks like \[4py=x^2\] where \(p\) is the distance between the vertex and the focus, or the vertex and the directrix in this case \(p=1\)

  17. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    your answer is therefore \[4y=x^2\]

  18. ckallerid
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Didn't I need to solve for Y or something like that?

  19. ckallerid
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    whatevs thanks guys!

  20. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.