- A) $x = 9 + 18 t , y = - \frac { 3 \sqrt { 2 } } { 2 } + \frac { 3 \sqrt { 2 } } { 2 } t , z = 5 + 10 t$

question 57

Multiple Choice

$\text { For the smooth curve } r ( t ) \text {, find the parametric equations for the line that is tangent to } r \text { at the given parameter value } t = t _ { 0 } \text {. }$
- $$\mathbf { r } ( \mathrm { t } ) = ( 9 \tan \mathrm { t } ) \mathbf { i } - ( 3 \sin \mathrm { t } ) \mathbf { j } + \left( 10 \cos ^ { 2 } \mathrm { t } \right) \mathbf { k } ; \mathrm { t } _ { 0 } = \frac { \pi } { 4 }$$

• A) \(x = 9 + 18 t , y = - \frac { 3 \sqrt { 2 } } { 2 } + \frac { 3 \sqrt { 2 } } { 2 } t , z = 5 + 10 t\)
• B) \(x = 9 + 18 t , y = - \frac { 3 \sqrt { 2 } } { 2 } - \frac { 3 \sqrt { 2 } } { 2 } t , z = 5 - 10 t\)
• C) \(x = 9 + 18 t , y = - \frac { 3 } { 2 } - \frac { 3 } { 2 } t , z = 10 - 10 t\)
• D) \(x = 18 + 9 t , y = - \frac { 3 \sqrt { 2 } } { 2 } - \frac { 3 \sqrt { 2 } } { 2 } t , z = - 10 + 5 t\)

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