Consider the Paraboloid $z = x ^ { 2 } + y ^ { 2 }$

Multiple Choice

Consider the paraboloid $z = x ^ { 2 } + y ^ { 2 }$ . Which of the following space curves have as their range points lying on this paraboloid?

A) r (t) = $\langle t \sin t , t \cos t , t \rangle , t \in \mathbb { R }$
B) r (t) = $\left\langle t ^ { 2 } , t \sin t , t \cos t \right\rangle , t \in \mathbb { R }$
C) r (t) = $\left\langle t \cos t , t \sin t , t ^ { 2 } \right\rangle , t \in \mathbb { R }$
D) r (t) = $( \sqrt { t } \sin t , t , \sqrt { t } \cos t ) , t > 0$

E) r (t) = $( \sqrt { t } \sin t , \sqrt { t } \cos t , t \} , t > 0$