Results 1 to 3 of 3

Math Help - Level Curves of xy/(x^2+y^2)

  1. #1
    Newbie
    Joined
    May 2011
    Posts
    12

    Level Curves of xy/(x^2+y^2)

    I am trying to find the level curves for the function g(x,y)= k = xy/(x^2+y^2).I get, x^2+y^2-xy/k=0. I know this is an ellipse, but I do not know how to factor, and find values of k for which the level curves exist.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,035
    Thanks
    49

    Re: Level Curves of xy/(x^2+y^2)

    Quote Originally Posted by dnftp View Post
    this is an ellipse
    No because you have minus xy, not minus constants ab, i.e.

    x^2+y^2-xy/k=0 - Wolfram|Alpha

    not

    ellipse - Wolfram|Alpha

    E.g. for k = 1/4

    x^2+y^2-4xy=0 - Wolfram|Alpha

    and k = 1/2

    x^2+y^2-2xy=0 - Wolfram|Alpha

    and k from -1/2 to 1/2

    z= (xy)/(x^2 + y^2) - Wolfram|Alpha
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2012
    From
    Denton, TX
    Posts
    1

    Re: Level Curves of xy/(x^2+y^2)

    Quote Originally Posted by dnftp View Post
    I am trying to find the level curves for the function g(x,y)= k = xy/(x^2+y^2).I get, x^2+y^2-xy/k=0. I know this is an ellipse, but I do not know how to factor, and find values of k for which the level curves exist.
    I think the quadratic equation works to solve for y in terms of x and k.

    y^2 - x/k y + x^2 = 0 -> y = \frac{x/k \text{ + or - } \sqrt{x^2/k^2 - 4x^2}}{2} (didn't know how to make the + or - symbol in tex)

    Check this as I did it in a hurry! I think the logic is sound, though.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. level curves
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: April 25th 2012, 08:10 AM
  2. level curves
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: May 14th 2009, 11:09 PM
  3. Level Curves
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 18th 2009, 08:39 PM
  4. level curves
    Posted in the Calculus Forum
    Replies: 6
    Last Post: July 9th 2008, 02:36 PM
  5. level curves
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 25th 2008, 12:30 AM

Search Tags


/mathhelpforum @mathhelpforum