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Math Help - Describe the level surfaces of the function

  1. #1
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    Describe the level surfaces of the function

    f(x,y,z)= x^2+ 3y^2+ 5z^2

    k=x^2+ 3y^2+ 5z^2 if k=0 we have a ellipsewith with origin 0,0
    when k>0 family of ellipses of one sheet
    K<0 family of ellipses

    I do not know if I am doing it right or if I am describing them exactly.
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  2. #2
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    Quote Originally Posted by andreaspohle View Post
    f(x,y,z)= x^2+ 3y^2+ 5z^2

    k=x^2+ 3y^2+ 5z^2 if k=0 we have a ellipsewith with origin 0,0
    when k>0 family of ellipses of one sheet
    K<0 family of ellipses

    I do not know if I am doing it right or if I am describing them exactly.
    If k > 0, then ellipsoid's, if k = 0, just one point at the origin and nothing for k< 0 .
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