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Math Help - Equation of curve of intersection (R3)

  1. #1
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    Equation of curve of intersection (R3)

    What is the equation of the curve of intersection of:

    z = x^2 + y^2 and

    2y + z = 0

    (Refer to attachment for graph of both equations).
    Attached Thumbnails Attached Thumbnails Equation of curve of intersection (R3)-graph.jpg  
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  2. #2
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    Please ignore the previous attachment.

    Refer to the correct attachment below.
    Attached Thumbnails Attached Thumbnails Equation of curve of intersection (R3)-graph-surfaces.png  
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  3. #3
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    Quote Originally Posted by SyNtHeSiS View Post
    What is the equation of the curve of intersection of:

    z = x^2 + y^2 and

    2y + z = 0
    .
    What have you tried yourself? Do you understand that, because this is a one dimensional curve in three dimensions, you will need to find three equations for x, y, and z in terms of a siingle parameter?

    Since z= x^2+ y^2, that second equation is 2y+ z= 2y+ x^2+ y^2= 0 which is the same as x^2+ y^2+ 2y+ 1= 1 or x^2+ (y+ 1)^2= 1. That is, the projection of that curve down to the xy-plane is the circle of radius 1 with center at (0, -1).

    Do you know how to parameterize such a circle? Use either z= x^2+ y^2 or z= -2y to complete the parametric equations for this curve.
    Last edited by HallsofIvy; March 6th 2011 at 04:26 AM.
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