Parameterize the Curve Which Lies on the Plane 5x - $x ^ { 2 } + y ^ { 2 } = 25$

Multiple Choice

Parameterize the curve which lies on the plane 5x - 10y + z = 6 above the circle $x ^ { 2 } + y ^ { 2 } = 25$

A) $\vec { r } ( t ) = 5 \sin t \vec { i } + 5 \cos t \vec { j } + ( 6 - 5 \sin t + 10 \cos t ) \vec { k }$
B) $\vec { r } ( t ) = 5 \sin t \vec { i } + 5 \cos t \vec { j } + ( 6 - 25 \sin t - 50 \cos t ) \vec { k }$
C) $\vec { r } ( t ) = 5 \sin t \vec { i } + 5 \cos t \vec { j } + ( 6 + 25 \sin t + 25 \cos t ) \vec { k }$
D) $\vec { r } ( t ) = 5 \sin t \vec { i } + 5 \cos t \vec { j } + ( 6 - 25 \sin t + 50 \cos t ) \vec { k }$
E) $\vec { r } ( t ) = 5 \sin t \vec { i } + 5 \cos t \vec { j } + ( 6 - 5 \sin t + 25 \cos t ) \vec { k }$