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Intersection of curves

  1. Jul 19, 2011 #1
    I need to find the point of intersection of the curves x^2 + y^2 =1, z= 0 and x=cost, y=sint, z=t. I plugged in the latter equation into the former and got (1,0,0) as an answer but I'm not exactly sure why that works, I can't visualize how plugging in the parts of a parametric equation will yield the point of intersection.

    I also need to find the tangent lines to the curves at that point, and I'm not sure where to start.
     
  2. jcsd
  3. Jul 19, 2011 #2

    hunt_mat

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    The two curves you have in the circle in the plane and a helix. You would expect that there is only one intersection point, and that will be at t=0.
     
  4. Jul 19, 2011 #3
    Makes sense. How do I find the tangent line to a parametric curve in R3, though?
     
  5. Jul 19, 2011 #4

    hunt_mat

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    Differentiate with respect to t!!!!
     
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