$(2$ marks$)$ Paramterizations need not be unique: Parametrize the curve $y=2x^2-3$ in two different ways $($i$.$e$.$ find two different vector$-$valued functions that describe the same curve$).$

$(2$ marks$)$ Show that the curve with parametric equations $x=sint,y=cost,z=si{n}^{2}t$ lies at the intersection of the surfaces $z=x^2$ and $x^2+y^2=1.$

$(2$ marks$)$ At what point does the helix $r(t)=(sint,cost,t)$ intersect the sphere $x^2+y^2+z^2=5?$