Find a Vector-Valued Function for the Hyperboloid $x ^ { 2 } + y ^ { 2 } - z ^ { 2 } = 121$

Multiple Choice

Find a vector-valued function for the hyperboloid $x ^ { 2 } + y ^ { 2 } - z ^ { 2 } = 121$

A) $\mathbf { r } ( u , v ) = u \cos v \mathbf { i } + u \sin v \mathbf { j } + \sqrt { u ^ { 2 } + 121 } \mathbf { k }$
B) $\mathbf { r } ( u , v ) = u \sin v \mathbf { i } + 11 u \cos v \mathbf { j } + \sqrt { u ^ { 2 } + 1 } \mathbf { k }$
C) $\mathbf { r } ( u , v ) = 11 u \sin v \mathbf { i } + u \cos v \mathbf { j } + \sqrt { u ^ { 2 } - 1 \mathbf { k } }$
D) $\mathbf { r } ( u , v ) = 11 u \cos v \mathbf { i } + 11 u \sin v \mathbf { j } + 11 \sqrt { u ^ { 2 } - 1 } \mathbf { k }$
E) $\mathbf { r } ( u , v ) = 11 u \cos \boldsymbol { i } + 11 u \sin v \mathbf { j } + 11 \sqrt { u ^ { 2 } - 121 } \mathbf { k }$