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Math Help - Parametrizing the Intersection of Surfaces

  1. #1
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    Parametrizing the Intersection of Surfaces

    Hello, I am stuck on this problem involving the parametrizing of two surfaces :

    Find a parametrization of the following curve:
    The intersection of the plane with the sphere

    r(t)= < ? , 7 , ?>

    I have gotten the second component which is simply 7, but that's as far as i have gotten, i know that the first and third are going to involve cos(t) and sin(t) respectivly, but how do i go about solving them?

    Thanks again!!
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    Quote Originally Posted by Esc View Post
    Hello, I am stuck on this problem involving the parametrizing of two surfaces :

    Find a parametrization of the following curve:
    The intersection of the plane with the sphere

    r(t)= < ? , 7 , ?>

    I have gotten the second component which is simply 7, but that's as far as i have gotten, i know that the first and third are going to involve cos(t) and sin(t) respectivly, but how do i go about solving them?

    Thanks again!!
    plug in y = 7 in the sphere and solve. you get x^2 + z^2 = 5^2 .......this is a circle of radius 5, how do we parameterize circles?
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    Quote Originally Posted by Jhevon View Post
    plug in y = 7 in the sphere and solve. you get x^2 + z^2 = 5^2 .......this is a circle of radius 5, how do we parameterize circles?
    i know that x^2 + z^2=5^2 is going to equal sin^2(x) + cos^2(x)=5^2 and i found the answer to be <5cos(t), 7, 5sin(t)> and it was corect!!!!

    Thank you soooo much!!!!
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Esc View Post
    i know that x^2 + z^2=5^2 is going to equal sin^2(x) + cos^2(x)=5^2 and i found the answer to be <5cos(t), 7, 5sin(t)> and it was corect!!!!

    Thank you soooo much!!!!
    very good!
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