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Math Help - Parametrization of Intersection.

  1. #1
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    Parametrization of Intersection.

    Have no idea how to solve this problem.

    Problem:
    Parameterize the curve of the intersection of the surfaces x^2+y^2=9 and z=x+2y the point (3,0,3) should correspond to the point t=0.

    The first equation is a circle of radius 3. So I know that paramterization should be
    x=3sin(t*pi)
    y=3cos(t*pi)

    No idea how to solve for the intersection of the two though.
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  2. #2
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    Re: Parametrization of Intersection.

    Quote Originally Posted by Bracketology View Post
    Have no idea how to solve this problem.

    Problem:
    Parameterize the curve of the intersection of the surfaces x^2+y^2=9 and z=x+2y the point (3,0,3) should correspond to the point t=0.

    The first equation is a circle of radius 3. So I know that paramterization should be
    x=3sin(t*pi)
    y=3cos(t*pi)

    No idea how to solve for the intersection of the two though.
    Since the point (3,0,3) should correspond to the point t=0, it should be

    x=3cos(t*pi)
    y=3sin(t*pi)

    in which case

    z=3cos(t*pi) + 6sin(t*pi)

    and that's the answer. Think about it.
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  3. #3
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    Re: Parametrization of Intersection.

    Quote Originally Posted by mr fantastic View Post
    Since the point (3,0,3) should correspond to the point t=0, it should be

    x=3cos(t*pi)
    y=3sin(t*pi)

    in which case

    z=3cos(t*pi) + 6sin(t*pi)

    and that's the answer. Think about it.

    That's it? Seems simple. I just haven't gotten the hang of parametrics yet. Luckily its another 6 weeks before our next test, so that gives me plenty time to learn. Thanks for the help!
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