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Math Help - Problem with traces defining a shape

  1. #1
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    Problem with traces defining a shape

    I have the equation x = y^2 + 4z^2

    and I am to use traces to sketch and identify the surface. This question is taken from Multivariable Calculus 6th Edition by James Stewart. I think I have to begin by setting z = 0. I then get x - y^2 = 0 which is the same as y = square root (x). This gives me a line in the xy plane which I think you can call an ellipse and the answer in the book says the 3-D figure to be obtained is an Elliptic paraboloid.

    However I can't get the horizontal or vertical traces because the only ones that make sense when I set x, y, or z equal to k are when the variables x,y,z = 0 and therefore produce the vectors <0,0,0>, <0,0,0>, <0,0,0>. I need some coordinates other than the origin if I want to sketch the shape.
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  2. #2
    MHF Contributor
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    You set z=0 to find the x = y^2 on the xy-plane, a parabola.

    Why not set y=0, to find x = 4z^2 on the xz-plane, another parabola ?

    On the yz-plane? None. When x=0, y^2 = -4z^2. Cannot be.
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