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Math Help - Parametrize curve of intersection of surfaces

  1. #1
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    Parametrize curve of intersection of surfaces

    Parametrice the curve of intersection of these surfaces (counterclockwise, viewpoint in positive z axis)

    z=3+x^2+y^2 , z=5-\sqrt{x^2+y^2}

    The only thing I did was equating x^2+y^2=2-\sqrt{x^2+y^2}. I have no clue of how to parametrize this.
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  2. #2
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    Quote Originally Posted by kodos View Post
    Parametrice the curve of intersection of these surfaces (counterclockwise, viewpoint in positive z axis)

    z=3+x^2+y^2 , z=5-\sqrt{x^2+y^2}

    The only thing I did was equating x^2+y^2=2-\sqrt{x^2+y^2}. I have no clue of how to parametrize this.
    I think it's easier to eliminate the x^2 +y^2.

    So x^2 +y^2 = (5-z)^2 and from the first z = 3 +(5-z)^2 giving z = 4 \; \text{and}\; z = 7 (the only one that make sense is the z= 4). So sub. this into either gives

    x^2 + y^2 = 1 with z = 4. Better?
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  3. #3
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    Much better, thank you. Now, assuming "viewpoint in positive z axis" means higher than z=4,

    x=2cost
    y=2sint
    z=4

    Is that what it means?
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