A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = −1

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

    have you any method to use for this question...?

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

    not really no

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

    so what methods do you know.. 1. find the focal length and then find the vertex... 2. use the distance formula..

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

    number 1

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

    ok.... so start by plotting the given information |dw:1437680444218:dw| so this tells me the parabola is concave up... does that make sense...

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

    yes

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

    ok... so the line of symmetry is x = -5 and the vertex is a units below the focus... where a = the focal length so |dw:1437680607256:dw|

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

    so the length between the focus and the directrix is 6

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

    the distance between the focus and directrix is 2a the vertex is midway between the vertex and directrix on the line of symmetry

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

    that's great so 2a = 6 therefore the focal length is a = 3 is that ok..?

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

    yes

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

    |dw:1437680777548:dw|

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

    so where do you think the vertex is located..?

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

    woud it be at (-5,2)

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

    perfect.... now to get the correct equation I use a standard form \[(x - h)^2 = 4a(y - k)\] (h, k) is the vertex and a is the focal length so the equation is \[(x + 5)^2 = 4 \times 3 (y - 2)\] so this can be simplified and rewritten in the form you need.

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

    hope it all makes sense

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

    Thank you, it really does help

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

    if you need it rewritten I'd use \[y = \frac{1}{12}(x + 5)^2 + 2\]

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

    That's exactly what I thought it was. Thank you so much

  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.