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

Selorm

It can be shown that the polar curve r=a\sin(\theta)+b\cos(\theta), where ab\ne 0, is a circle. Find the center (in Cartesian coordinates) and radius of this circle in terms of a and b. x-coordinate of center: y-coordinate of center: Radius:

  • one year ago
  • one year ago

  • This Question is Closed
  1. ivanmlerner
    Best Response
    You've already chosen the best response.
    Medals 0

    What is ab\ne 0?

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

    r=a sin (theta) + b cos (theta), ab is not = 0

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

    Do you agree, that in cartesian coordinates the radius is \[\sqrt{(x-x_0)^2+(y-y_0)^2}\]Where (x0, y0) is the center?

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

    yea

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

    You could write it as a Cartesian equation by using cos(theta)=x/r and sin(theta)=y/r and r^2=x^2+y^2

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

    where does a and b come in?

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

    i know that multiplying the equation by r is a legitimate step that can get me r^2=a rsin (theta) + b rcos (theta). Is that right?

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

    Yeah sure you can do that.

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

    this can give r^2= ay + bx right?

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

    Ok and r^2=x^2+y^2

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

    yes

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

    so that will give x^2+y^2=ay+bx

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

    ok and write that equation in this form: (x-h)^2+(y-k)^2=r^2 where (h,k) is center and r is radius

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

    so meaning (x-b)^2+(y-a)^2

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

    ?

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

    hmm....I don't you completed the square right

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

    I mean you didn't complete the square...

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

    come again

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

    \[x^2-bx+y^2-ay=0\] you must complete the square honestly you made some rules up or something

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

    ok

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

    can u help with that?

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

    \[x^2+cx+(\frac{c}{2})^2=(x+\frac{c}{2})^2\]

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

    why (c/2)^2 and not (cx/2)^2?

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

    \[(x+\frac{c}{2})^2=(x+\frac{c}{2})(x+\frac{c}{2})=x(x+\frac{c}{2})+\frac{c}{2}(x+\frac{c}{2})\] \[=x^2+\frac{c}{2}x+\frac{c}{2}x+(\frac{c}{2})^2=x^2+cx+(\frac{c}{2})^2\]

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

    ok

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

    what next?

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

    \[x^2-bx+y^2-ay=0 \]

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

    You need to complete the square for both the x part and the y part.

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

    so we get (x+c/2)^2+(y+b/2)^2=0?

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

    then what next? equate each part to 0?

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

    hmmm.... So you have x^2-bx+b/2=(x-b/2)^2

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

    But whatever you add to one side you add to the other .

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

    x=b/2,y =a/2 and r=sqrt(a^2+b^2)/2

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

    YEP that is right.

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

    thank you

    • 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.