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    Hello,

    I need classify the following equation in affine space
    I think this means to give the type of surface it is...

    Im not sure how to go about doing this... I am aware of the matrix representation of such equations... maybe I could use Gauss Jordan on it and simplify the equations?

    Im really not sure

    Any ideas relating to this?
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    (Original post by number23)
    Hello,

    I need classify the following equation in affine space
    I think this means to give the type of surface it is...

    Im not sure how to go about doing this... I am aware of the matrix representation of such equations... maybe I could use Gauss Jordan on it and simplify the equations?

    Im really not sure

    Any ideas relating to this?
    not my field of expertise

    but I think this is a hyperboloid of two sheets shifted (if you complete the square in z)
    its axis of symmetry is the z axis and is shifted up this axis by 1
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    (Original post by TeeEm)
    not my field of expertise

    but I think this is a hyperboloid of two sheets shifted (if you complete the square in z)
    its axis of symmetry is the z axis and is shifted up this axis by 1
    thanks for the response
    how did you come to that answer?
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    (Original post by number23)
    thanks for the response
    how did you come to that answer?
    just facts i.e. that is the standard form of a hyperboloid of two sheets

    it is like saying how can you tell (x-2)2+(y-2)2 =4 represents a circle

    x2/a2 - y2/b2 -z2/c2 = 1

    is a hyperboloid of 2 sheets with axis of symmetry the x axis

    think of a 2D hyperbola rotated fully in the x axis
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    (Original post by TeeEm)
    just facts i.e. that is the standard form of a hyperboloid of two sheets

    it is like saying how can you tell (x-2)2+(y-2)2 =4 represents a circle

    x2/a2 - y2/b2 -z2/c2 = 1

    is a hyperboloid of 2 sheets with axis of symmetry the x axis

    think of a 2D hyperbola rotated fully in the x axis
    ok cheers, i didnt think of completing the square bit anyways

    im going to learn the equations tbh
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    (Original post by number23)
    ok cheers, i didnt think of completing the square bit anyways

    im going to learn the equations tbh
    note that after you complete the square you move x and y bit to the "z side" to leave the 1 positive.

    your hyperboloid is symmetrical in the z axis and translated down the z axis by 1.

    good luck
 
 
 
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