$(6$ marks$)$ Find a vector$-$valued function $($i$.$e$.$ parametrization$)$ that represents the curve of intersection of the two surfaces:

$($a$)$ The cylinder $x^2+y^2=4$ and the surface $z=xy$

$($b$)$ The paraboloid $z=4x^2+y^2$ and the parabolic cylinder $y=x^2$

$($c$)$ The semiellipsoid $x^2+y^2+4z^2=4,y0$ and the cylinder $x^2+z^2=1.$