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Math Help - level curves

  1. #1
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    Exclamation level curves

    for f(x,y) = 1 -2x^2 - 3y^2
    just wondering if someone could please help me find the equation of the curve of intersection of the surface z=f(x,y) with the plane x=1
    i can sketch the levelcurves for valuesof c and sketch the cross sections of the surface in the xz and yz planes, will that help?
    i couldn't find an example of how to do this type of question in my notes or textbook, so any help would be much appreciated!
    Last edited by mathshelpbook; May 24th 2008 at 11:49 PM.
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  2. #2
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    Quote Originally Posted by mathshelpbook View Post
    for f(x,y) = 1 -2x^2 - 3y^2
    just wondering if someone could please help me find the equation of the curve of intersection of the surface z=f(x,y) with the plane x=1
    i can sketch the levelcurves for valuesof c and sketch the cross sections of the surface in the xz and yz planes, will that help?
    i couldn't find an example of how to do this type of question in my notes or textbook, so any help would be much appreciated!
    1. The graph of f is a paraboloid

    2. The intersection of the paraboloid with a plane parallel to the axis of the paraboloid must be a parabola.

    3. Use parametric equation to get the intersection parabola:

    \left|\begin{array}{l}x=1 \\ y=t \\z=-1-3t^2\end{array}\right.

    4. I've attached a drawing of f and the cutting plane. Because it is very difficult to detect the parabola in this drawing I've sketched the parabola alone in a separate coordinate system.
    Attached Thumbnails Attached Thumbnails level curves-paraboloid_ebene.gif  
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