Level Curves

  1. hi... I am new to this topic and frustrated.

    I have a curve f(x,y)= -3y/(x2 +y2 + 1)

    I was asked to draw a level curve of this and I'm not getting anywhere with it. If anyone has any pointers, or can help me with solving this question I would be gretfull. The only other thing this question asks is to describe it at the orgin or at (0,3) ( which is steeper).

    thanks for any help.
  2. jcsd
  3. Level curves are curves where the function is constant, and equals lets say to a number c.

    So you get an equation


    Rearranging this gives you


    Now you just have to investigate different values of c.
  4. HallsofIvy

    HallsofIvy 41,260
    Staff Emeritus
    Science Advisor

    That should be [itex]c(y- 3/(2c))^2[/itex]. That is, that leading "c" should be outside the parentheses.

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