Find a vector function that represents the curve of intersection of the two surfaces

  1. 1. The problem statement, all variables and given/known data

    Find a vector function that represents the curve of intersection of the two surfaces:
    The cone z = sqrt( x^2 + y^2) and the plane z = 1+y.

    2. Relevant equations

    z = sqrt( x^2 + y^2) and the plane z = 1+y.

    3. The attempt at a solution
    This problem can be solved as following using x as the parameter.
    x^2+y^2 = z^2 = (1+y)^2 = 1+2y+y^2. => x^2 = 1 + 2y.

    x=t; y = (t^2-1)/2; z = 1+(t^2-1)/2 = (t^2+1)/2

    My question is, what if we use y as the parameter,

    i get ,

    y=t, x=(2t+1)^(1/2) z=t+1,

    is this answer also correct?
     
    Last edited by a moderator: Feb 4, 2013
  2. jcsd
  3. Dick

    Dick 25,852
    Science Advisor
    Homework Helper

    Re: Vectors

    Sure, with the proviso that it only represents part of the curve. For example, points with negative values of x won't appear in the second parametrization (where you also should specify t>=(-1/2)). You'd need the x=(-(2t+1)^(1/2)) solution as well to get them all.
     
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