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

Callisto

Haven't done circle for long :( In the figure, a circle S: \(x^2+y^2+6x-2y=0\) cuts the axes at the origin O, A and C. A point B lies on the circle S so that the length of BC is \(2 \sqrt{5}\) units. BC is produced to cut the x-axis at D. Find the coordinates of B

  • one year ago
  • one year ago

  • This Question is Closed
  1. Callisto
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1356781451262:dw|

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

    brb

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

    solve these equations for \( x_1, y_1 \), \[ x_1^2 + y_1^2 + 6x_1−2y_1=0,\\ x_2^2 + y_2^2 + 6x_2 - 2y_1 = 0, x_2=0, y_2 \neq 0 \\ (x_1-x_2)^2 + (y_1-y_2)^2 = 20\]

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

    May I know what (x2, y2) is??

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

    x_2, y_2 are the coordinates of C

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

    probably you would end up with two sets of point, choose the the point where y>0

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

    sorry ... this equation .. change y1 to y2 \[ x_2^2 + y_2^2 + 6x_2 - 2y_1 = 0, x_2=0, y_2 \neq 0 \\ \]

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

    Algebra matters.

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

    C = (0, 2)

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

    yes!! sorry i was careless ... did you find out answer?

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

    \(x^2 + y^2 +6x - 2y =0\) ---(1) \(x^2+(y-2)^2 =20\) => \(x^2 + y^2 -4y+4 =20\) ---(2)

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

    he?

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

    Do you mean I knew the answer?

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

    I knew the answer, yes. I'm looking for a way to get the answer. I tried once (more than once) but I thought I was making it too complicated. I just wanted to find a simpler way so that my sister can do it easily.

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

    co-ordinates of A can also be found similarly.

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

    A = (-6, 0)

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

    D = (4, 0)

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

    then u know equation of line BD can't u use that to find co-ordinates of B ?

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

    solving equation of line and circle simultaneously.

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

    are u sure about D =(4,0)??

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

    equation of line BD: \[\frac{y-2}{x} = \frac{2}{-4}\]\[x = 4-2y\] \[(4-2y)^2 + y^2 +6(4-2y) - 2y =0\] \[5y^2 - 30y + 40=0\]\[y=4, 2\]When y=4, x = 4-2(4) = -4 When y=2, x=4-2(2) =0 (rejected) So, B= (-4, 4) Yay! Much simpler :) Thanks!!! @hartnn Yes! Yes! D = (4,0)

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

    oh, i somehow got 36 instead of 40, thats why i was stuck.....

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

    Correction: o.O Did I make a mistake? :S

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

    no, u are correct.

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

    Okay, thanks again! I didn't thought of the line. I'm just too stupid :(

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

    happens! i just did a silly mistake of 6*4 =20 :P

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

    did anyone notice : |dw:1356789155290:dw|

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

    where thats the center we know co-ordinates of C let center be O hence we know slope of OB slope given, distance give, we can find co-ordinate! B)

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

    how do we know slope of OB?

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

    ohh..

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

    as we know slope of OC

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

    yep..exactly..

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

    given slope of OB and O, we can find B, no need of any distance..

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

    Not so relevant. |dw:1356789503661:dw|

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

    ohh yes!! COA are collinear !

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

    how does that make it any simpler ?

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

    i dont know,,just a good fact to know! :D

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

    ''Not so relevant.'' :P

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

    :P ok ..

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

    u got 2 more easy methods ;)

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

    Yes! Yes! Thanks! Thanks!!

    • 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.