Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Callisto

  • 2 years ago

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

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

    |dw:1356781451262:dw|

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

    brb

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

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

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

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

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

    x_2, y_2 are the coordinates of C

  6. experimentX
    • 2 years ago
    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

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

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

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

    Algebra matters.

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

    C = (0, 2)

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

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

  11. Callisto
    • 2 years ago
    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)

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

    he?

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

    Do you mean I knew the answer?

  14. Callisto
    • 2 years ago
    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.

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

    co-ordinates of A can also be found similarly.

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

    A = (-6, 0)

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

    D = (4, 0)

  18. hartnn
    • 2 years ago
    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 ?

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

    solving equation of line and circle simultaneously.

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

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

  21. Callisto
    • 2 years ago
    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)

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

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

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

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

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

    no, u are correct.

  25. Callisto
    • 2 years ago
    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 :(

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

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

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

    did anyone notice : |dw:1356789155290:dw|

  28. shubhamsrg
    • 2 years ago
    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)

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

    how do we know slope of OB?

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

    ohh..

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

    as we know slope of OC

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

    yep..exactly..

  33. hartnn
    • 2 years ago
    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..

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

    Not so relevant. |dw:1356789503661:dw|

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

    ohh yes!! COA are collinear !

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

    how does that make it any simpler ?

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

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

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

    ''Not so relevant.'' :P

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

    :P ok ..

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

    u got 2 more easy methods ;)

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

    Yes! Yes! Thanks! Thanks!!

  42. 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.