Find a Parametric Representation of the Curve of Intersection of the Paraboloid

Multiple Choice

Find a parametric representation of the curve of intersection of the paraboloid z = x² + y² and the plane 8x - 4y - z - 11 = 0.

A) r = (3 - 4cos(t) ) i + (3 + 2sin(t) ) j + (1 - 32cos(t) - 8sin(t) ) k, 0 $\le$ t $\le$ 2 $\pi$
B) r = (3 + 4cos(t) ) i + (3 - 2sin(t) ) j + (1 + 32cos(t) + 8sin(t) ) k, 0 $\le$ t $\le$ 2 $\pi$
C) r = (4 + 3cos(t) ) i + (-2 + 3sin(t) ) j + (24cos(t) - 12sin(t) - 29) k, 0 $\le$ t $\le$ 2 $\pi$
D) r = (-4 + 3cos(t) ) i + (2 + 3sin(t) ) j + (24cos(t) - 12sin(t) - 51) k, 0 $\le$ t $\le$ 2 $\pi$
E) r = (-3 + 4cos(t) ) i + (-3 - 2sin(t) ) j + (32cos(t) + 8sin(t) - 23) k, 0 $\le$ t $\le$ 2 $\pi$