Find a vector function that represents the curve of intersection of the paraboloid and the cylinder . Use the variable t for the parameter.
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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 $\displaystyle y= 3x^2= 3t^2$ so that gives you the second component. Finally, $\displaystyle z= 9x^2+ 4y^2= 9x^2+ 4(3x^2)^2= 9x^2+ 36x^4$ and, since x= t, $\displaystyle z= 9t^2+ 36t^4$. The vector is $\displaystyle <t, 3t^2, 9t^2+ 36t^4>$.