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Math Help - Vector-Valued Functions

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    Vector-Valued Functions

    Find a vector function that represents the curve of intersection of the paraboloid and the cylinder . Use the variable t for the parameter.
    ____,____


    Thanks.
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    Quote Originally Posted by jffyx View Post
    Find a vector function that represents the curve of intersection of the paraboloid and the cylinder . Use the variable t for the parameter.
    ____,____


    Thanks.
    This is much easier than you think! The fact that your answer starts "< t, " tells you that really are using x itself as the parameter. And you are told that y= 3x^2= 3t^2 so that gives you the second component. Finally, z= 9x^2+ 4y^2= 9x^2+ 4(3x^2)^2= 9x^2+ 36x^4 and, since x= t, z= 9t^2+ 36t^4. The vector is <t, 3t^2, 9t^2+ 36t^4>.
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