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

question 48

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