Answer
Elliptical cylinder
$\frac{x^{2}}{9}+z^{2}=1$ ($-1\le y \le1$)
Work Step by Step
Given: $r(s,t)=\lt 3 cost, s, sint\gt$
Write the vector equation in its equivalent parametric equations:
$x=3 cost $, $y= s $ and $z=sint$
Solving the first parametric equation yields:
$\frac{x}{3}= cost $
Therefore,
$\frac{x^{2}}{3^{2}}+z^{2}= cos^{2}t +sin^{2}t$
$\frac{x^{2}}{3^{2}}+z^{2}=1$
which represents as a equation of a Elliptical cylinder.
