Equation of a quadric surface on which this curve lies? I am currently learning about surfaces. So for the parametrized curve: 
$r=\langle t^2, 3t\cos(2t), 3t\sin(2t)\rangle,\quad t\ge 1$
how can I find a equation for the surface the curve lie? Also what kind of surface? Is it a paraboloid, hyperboloid of one sheet, hyperboloid of two sheets, etc. How can you tell which one it is?
Can someone please explain step by step this to me?

Notice that, by the usual trigonometric identity, 
$$y^2+z^2 = 9x$$ 
i.e. 
$$\dfrac{y^2}{3^2}+\dfrac{z^2}{3^2} - x = 0$$
Which would normally be a circular paraboloid extending in the $x$-direction. (Easily seen by noting that, for any fixed $x$, we have a circle of radius $3\sqrt x$ in the plane that is parallel to the $y,z$-plane at a distance $x$ from it.)
However, the parameterisation given forces exactly two values of $t$ for any fixed $x$ (namely $t=\pm \sqrt x$), where each yields exactly two points as opposed to a full circle for any fixed $x$. It follows that this curve is some kind of helical object of two strands.
