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Math Help - finding the traces in each coordinate plane

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    42

    Exclamation finding the traces in each coordinate plane

    how do you find the traces of the equation x=y(squared)+4z(squared) ?
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  2. #2
    Newbie
    Joined
    Sep 2009
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    10
    i believe you set y=0, and then z=0 and then x equal to, say, 1. separately.
    so you get x=4z^2
    x=y^2
    and
    y^2 + 4z^2 = 1

    then to draw,

    first look at the first equation.
    you need to look at the xz plane.
    and this will be a narrow parabola (x=4z^2)
    (it should be opening up along the x axis)

    then look at the next equation.
    it will be on the xy plane.
    x=y^2 is another parabola (it should be opening up along the x axis again, but this one will probably be flat, unlike the first - depending on how you drew your axes)

    now look at your third equation - this is an ellipse. (the equation is similar to that of a circle, but it will be stretched longer in the y direction)
    so now look at your graph, and go to x=1. basically, at x=1, you're going to have an ellipse in the yz plane.

    connect the "traces" and you'll get something that looks like Paraboloid - Wikipedia, the free encyclopedia in some direction.

    i hope that helps!
    i only just learned this myself a week or two ago, so i may have made a mistake. but i hope this gives an idea.
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