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Math Help - surfaces and solids

  1. #1
    n22
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    surfaces and solids

    Hello people,

    I am finding it hard to recognize the difference between paraboloids,cylinders,cones and etc..(any 3d surfac)
    How do I tell the difference between them?
    for example y^2+4z^2=9 where does this curve open up..how do i tell?
    I know I am asking stupid questions ..
    thanks
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: surfaces and solids

    That will be an ellipse on the plane x = 0. Do you see that it is a 2D curve since there are only 2 variables?
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  3. #3
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    Re: surfaces and solids

    Quote Originally Posted by MarkFL View Post
    That will be an ellipse on the plane x = 0. Do you see that it is a 2D curve since there are only 2 variables?
    wrong aproach...............see the figure below.

    surfaces and solids-figure001.png
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  4. #4
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    Re: surfaces and solids

    Quote Originally Posted by MarkFL View Post
    That will be an ellipse on the plane x = 0. Do you see that it is a 2D curve since there are only 2 variables?
    There are only two variables in this equation- that does not necessarily mean that we are to assume only two dimensions. If we are given that this is a 3D situation then it is "y^2+ 4z^2= 9 for all x" and is an elliptic cylinder whose axis is the x-axis.
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