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Homework Help: Intersection of paraboloid and normal line

  1. Oct 9, 2011 #1
    1. The problem statement, all variables and given/known data
    Where does the normal line to the paraboloid z=x^2+y^2 at the point (1,1,2) intersect the paraboloid a second time?

    2. Relevant equations

    3. The attempt at a solution

    I found the normal line to be 0=2x+2y-1, but I'm not sure what to do next.
  2. jcsd
  3. Oct 9, 2011 #2


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    Gold Member

    find the two points that satisfy both equations

    However, a quick look at your line equation suggests to me that it is the equation of a plane that is normal to the xy plane so the solution would be a 2D parabola; not what you're looking for.
  4. Oct 9, 2011 #3
    Is there any you recommend I should try and do?
  5. Oct 9, 2011 #4


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    Gold Member

    first find the LINE asked for, not a plane (which isn't what was asked for) and then do what I suggested in post #2

    EDIT: you say you have found the line. Post your work so we can help you see where you went wrong and got a plane instead.
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