# Math Help - Vector-Valued Functions

1. ## 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.

2. Originally Posted by jffyx
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 $$.