Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

artofspeed

Find the center and radius of this equation of circle x^2+y^2-ax+by=0

  • one year ago
  • one year ago

  • This Question is Closed
  1. AccessDenied
    Best Response
    You've already chosen the best response.
    Medals 1

    Well, this doesn't look like much of a nice circle equation. I prefer \((x - h)^2 + (y - k)^2 = r^2\), which has center (h, k), and radius r. I think if we can write it like that, we'll have more progress! Are you familiar with completing the square in quadratics?

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

    i got (x-a)^2 + (y+b)^2 = (a/2)^2 + (b/2)^2

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

    so the radius must be \[\sqrt{(a/2)^2 + (b/2)^2}\] and center is (a, -b) right?

    • one year ago
  4. AccessDenied
    Best Response
    You've already chosen the best response.
    Medals 1

    I think I agree with your radius, but if we expand out (x - a)^2, we'd get x^2 - 2a x + a^2. Instead, I think (x - a/2)^2 would be more accurate. It expands to x^2 - a/2 x - a/2 x + (a/2)^2 = x^2 - a x + (a/2)^2, what we originally had.

    • one year ago
  5. AccessDenied
    Best Response
    You've already chosen the best response.
    Medals 1

    * and similarly for y's perfect square.

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

    isn't x^2 - 2a x + a^2 = (x - a)^2 ?

    • one year ago
  7. AccessDenied
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes, that is correct. However, we had 'x^2 - ax' in our original equation, and added on a (a/2)^2 at the end. :)

    • one year ago
  8. AccessDenied
    Best Response
    You've already chosen the best response.
    Medals 1

    Like, we were aiming for a form of x^2 + 2w x + w^2 = (x + w)^2 when we added that (a/2)^2. Let w = -a/2, and we have: x^2 + 2(-a/2) x + (-a/2)^2 = (x - a/2)^2 x^2 - ax + (a/2)^2 = (x - a/2)^2 If that makes more sense.

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

    o-o so how can i improve my answers

    • one year ago
  10. AccessDenied
    Best Response
    You've already chosen the best response.
    Medals 1

    Instead of (x - a)^2 + (y + b)^2 = ... (the rest I believe is correct so i won't copy it), we'd have (x - a/2)^2 + (y + b/2)^2 = ... (same thing)

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

    so instead of writing \[(x-a)^2 + (y+b)^2 = (a/2)^2 + (b/2)^2\] what do you suggest o-o

    • one year ago
  12. AccessDenied
    Best Response
    You've already chosen the best response.
    Medals 1

    \[ (x - \frac{a}{2})^2 + (y + \frac{b}{2})^2 = (a/2)^2 + (b/2)^2 \] If it doesn't make sense where those come from, you can expand it out to prove that this is our original problem and that yours doesn't quite come out to be the same. I think its just an error with how you originally completed the square; you added the right term, but you collected it into (x - a)^2 and (y + b)^2, which wouldn't be the same thing..

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

    ohhhh ok yea i got it.. sorry for being dumb lol

    • one year ago
  14. AccessDenied
    Best Response
    You've already chosen the best response.
    Medals 1

    It's fine. We learn best from mistakes. :) So, from there, you can pull the information pretty easily. I may recommend a small detail on the radius: when you take the square root, you could factor out that 1/2^2 from (a/2)^2 + (b/2)^2 and pull it out as a 1/2. It'd look nicer, I think. :P 1/2 sqrt(a^2 + b^2)

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

    oh yea true

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

    thx man

    • one year ago
  17. AccessDenied
    Best Response
    You've already chosen the best response.
    Medals 1

    You're welcome! :)

    • one year ago
    • Attachments:

See more questions >>>

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.