1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Eliminating variables

  1. Mar 17, 2010 #1
    1. The problem statement, all variables and given/known data

    I have the equations x = a * sinh(u) / (cos(v) + cosh(u)) and y = a * sin(v) / (cos(v) + cosh(u)). I believe that if a value of u is fixed, then the locus of (x,y) satisfying these equations is a circle depending on v. Similarly, I believe that if a value of v is fixed, then the locus of (x,y) satisfying these equations is a circle depending on u.

    I would like to verify this.

    2. Relevant equations



    3. The attempt at a solution

    It seems the easiest way is to find the equations of the circles by somehow eliminating either u or v, but I can't figure out how. I've employed various identities, such as cosh^2 - sinh^2 = 1, but I can never fully eliminate one variable.
     
  2. jcsd
  3. Mar 17, 2010 #2
    The coordinate system I'm working with is slightly different, but my conjecture about the level curves for u = const. and v = const. is based off this Wikipedia article: http://en.wikipedia.org/wiki/Bipolar_coordinates

    I cannot figure out, however, how Wikipedia managed to derive the equations in the section "Curves of constant sigma and tau." I suspect a similar method will work in my case.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook