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Space Curve Intersecting a Parabloid

  1. Feb 24, 2013 #1
    1. The problem statement, all variables and given/known data

    At what point does the curve [itex]\vec{r}(t) = <t,0,2t-t^2>[/itex] intersects the paraboloid [itex]z=x^2+y^2[/itex]

    2. Relevant equations

    None Known

    3. The attempt at a solution

    I assume that it might be easier to parametrize [itex]z=x^2+y^2[/itex], but I'm not sure how to do that or if there's a more standard approach.

    I missed a day of class and I can't find any examples more than vaguely similar to this in the book. :\

    Thanks for any help!
  2. jcsd
  3. Feb 24, 2013 #2
    You can also try to de-parameterize ##\vec r(t)##. Hint: there won't be any y terms.
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