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Math Help - sketch quadric surfaces

  1. #1
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    Question sketch quadric surfaces

    I am very poor in graphing quadric surfaces. ( without any help of a tool - like a computer program).

    Could you please teach me the technique and steps of graphing quadric surfaces? Thank you very much.

    Here is my first example.
    Question 1)
    Identify and sketch the quadric surface

    y^2 -(x^2/4) -(z^2/9) =1
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  2. #2
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    Quote Originally Posted by Jenny20 View Post
    I am very poor in graphing quadric surfaces. ( without any help of a tool - like a computer program).

    Could you please teach me the technique and steps of graphing quadric surfaces? Thank you very much.

    Here is my first example.
    Question 1)
    Identify and sketch the quadric surface

    y^2 -(x^2/4) -(z^2/9) =1
    I'm rather bad at this too. Here's what has helped me in the past.

    Consider the projection of this surface onto the xy, yz, and xz planes.
    For the xy plane, set z = 0:
    - \frac{x^2}{4} + y^2 = 1
    This is a hyperbola with an axis of symmetry along the y-axis and vertices at (0, \pm 1, 0).

    For the yz plane set x = 0:
    y^2 - \frac{z^2}{9} = 1
    This is a hyperbola with an axis of symmetry along the y-axis and vertices at (0, 0, \pm 3).

    For the xz plane, set y = 0:
    -\frac{x^2}{4} - \frac{z^2}{9} = 1
    This is a hyperbola with an axis of symmetry along the x-axis and vertices at (\pm 2, 0, 0).

    Now the challenge is trying to put this together in 3D. That I can't help you with, but you should have at least a rough idea of what's going on.

    -Dan
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    Hi Dan,

    Thank you very much.

    Is it a must to master the skill of graphing 3-D pictures (without the help of a graphic calculator or computer) in the multivariable calculus courses?

    I usually do the graph with a computer or calculator.
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Jenny20 View Post
    Hi Dan,

    Thank you very much.

    Is it a must to master the skill of graphing 3-D pictures (without the help of a graphic calculator or computer) in the multivariable calculus courses?

    I usually do the graph with a computer or calculator.
    I'll admit I tended to cheat a bit, and my Engineering Graphics class was a disaster. My visualization skills do NOT extend beyond 2D. (Very bad attribute for a Physicist!)

    -Dan
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    Hi Dan,

    The same problem goes to me - visualizing a 3d picture is very difficult.

    What about the below question? Could you please teach me how to sketch it too? Thank you very much.

    Question
    Sketch the graph of the hyperboloid of two sheets.
    z^2 -x^2 -(y^2/4)=1
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Jenny20 View Post
    Hi Dan,

    The same problem goes to me - visualizing a 3d picture is very difficult.

    What about the below question? Could you please teach me how to sketch it too? Thank you very much.

    Question
    Sketch the graph of the hyperboloid of two sheets.
    z^2 -x^2 -(y^2/4)=1
    All I can do to guide you is the method I showed you before. (Frankly, it's the only trick I know.) Sketch what the projections onto the xy, yz, and xz planes look like and then try to put them together in 3D. Like the previous example all 3 projections are going to be hyperbolas.

    -Dan
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  7. #7
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    Graphing Quadradic Surfaces is easy (If you are not rotating). You need to memorize the different types. Then you do not need to use traces. There are only 6 and the formula makes sense so it is not as bad as you think.
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