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Homework Help: Finding parametric equations of a tangent line

  1. Dec 13, 2008 #1
    1. The problem statement, all variables and given/known data

    Find parametric equations of the tangent line at the point (-2,2,4) to the curve of intersection of the surface z=2x2-y2 and the plane z=4

    2. Relevant equations

    Not sure


    3. The attempt at a solution

    Not sure quite how to approach this. take the gradient of 2x^2-y^2 and just plug for x=rcos[tex]\Theta[/tex] and y=r sin[tex]\Theta[/tex] ?

    That seems too simple..
     
  2. jcsd
  3. Dec 13, 2008 #2

    Dick

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    The gradient gives you a normal direction for each surface. Then the tangent is perpendicular to both normals. How can you find a vector perpendicular to two other vectors?
     
  4. Dec 13, 2008 #3
    so I would end up with 4x-2y and zero for the two normal vectors? and then take the cross product of the two? I think I may be confusing some concepts here.
     
  5. Dec 13, 2008 #4

    Dick

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    Probably. The gradient is a vector. Those don't look like vectors. Better check the definition of 'gradient'.
     
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