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Simplifying Ellipse equation?

  1. Jun 8, 2010 #1
    1. The problem statement, all variables and given/known data

    Describe the shape of each level curve for the following function:

    z= (5x^2+y^2)^.5-2x


    2. Relevant equations

    I would like to prove that the curves are elliptical by setting z as a constnat and algebraically putting the equation in standard for for an ellipse Ax^2+By^2=R^2


    3. The attempt at a solution

    After squaring both sides, I get to:

    z^2+4xz=x^2+y^2

    I do not know how to isolate the z on one side from there. Any suggestions? I feel like this is a really obvious algebra trick that I am forgetting.

    Thank you very much for any help.
     
  2. jcsd
  3. Jun 8, 2010 #2

    hotvette

    User Avatar
    Homework Helper

    Two suggestions:

    - think of z as a number (that is arbitrary). No reason to isolate it

    - Use the equation of the general conic Ax2+Bxy+Cy2+Dx+Ey+F=0
     
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