Find a Parametrization of the Ellipse in Which the Plane $\theta$

Multiple Choice

Find a parametrization of the ellipse in which the plane z = 3y intersects the cylinder + = 4, using the polar angle $\theta$ in the xy-plane as the parameter, [0, 2 $\pi$ ] as parameter interval, and ensuring that the ellipse is oriented counterclockwise as viewed from high on the z-axis.

A) r = 2 cos( $\theta$ ) i + 2 sin( $\theta$ ) j + 6 sin( $\theta$ ) k
B) r = 2 cos( $\theta$ ) i - 2 sin( $\theta$ ) j + 6 sin( $\theta$ ) k
C) r = 2 cos( $\theta$ ) i + 2 sin( $\theta$ ) j - 6 sin( $\theta$ ) k
D) r = 2 cos( $\theta$ ) i - 2 sin( $\theta$ ) j - 6 sin( $\theta$ ) k
E) r = 2 cos( $\theta$ ) i + 2 sin( $\theta$ ) j + 3 sin( $\theta$ ) k