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Tangent Space of Singel layered hyperboloid

  1. Nov 11, 2007 #1
    Tangent space of single layered hyperboloid

    Ok i´m given a single layered hyperboloid given by [tex]\left(\frac{x}{a}-\frac{z}{c}\right)\cdot\left(\frac{x}{a}+\frac{z}{c}\right)-\left(1-\frac{y}{b}\right)\cdot\left(1+\frac{y}{b}\right)=0[/tex]

    Now the Problem asks me to take this as a vanishing determinant, i guess they mean

    [tex]\begin{vmatrix} \frac{x}{a}-\frac{z}{c} &1-\frac{y}{b} \\ 1+\frac{y}{b} & \frac{x}{a}+\frac{z}{c} \end{vmatrix}=0[/tex]


    Now out of the knowledge that the surface is parametrized by a vanishing determinant i should find 2 streight lines through every point p in the surface.

    Now im totally lost how to do it by the determinant.

    Im perfectly fine with just taking the tangent space at p and the just look for the direction vectors that produce lines entirely in the surface but how to do it this way.

    I thought of i as a Jacobian of some function (of a,b,c ?? )for whitch the hyperboloid is sort of a level set but i don´t know how to go on sorry some hint would be fine :)
    Thanks
     
    Last edited: Nov 11, 2007
  2. jcsd
  3. Nov 13, 2007 #2
    come on you guys :)
     
  4. Nov 13, 2007 #3
    Ok solved it :=)
     
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