Find a Vector-Valued Function, Using the Given Parameter, to Represent $\begin{array}{ll}\text { Surfaces } & \text { Parameter } \\z=\frac{x^{2}}{25}+\frac{y^{2}}{64}, y+8 x=0 & x=t\end{array}$

question 23

Multiple Choice

Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. $\begin{array}{ll}\text { Surfaces } & \text { Parameter } \\z=\frac{x^{2}}{25}+\frac{y^{2}}{64}, y+8 x=0 & x=t\end{array}$

• A) \(\mathbf { r } ( t ) = t \mathbf { i } - 8 t \mathbf { j } + \frac { 25 } { 26 } t ^ { 2 } \mathbf { k }\)
• B) \(\mathbf { r } ( t ) = t \mathbf { i } + \frac { 26 } { 25 } t ^ { 2 } \mathbf { j } - 8 t \mathbf { k }\)
• C)\(\mathbf { r } ( t ) = t \mathbf { i } + 8 t \mathbf { j } + \frac { 26 } { 25 } t ^ { 2 } \mathbf { k }\)
• D)\(\mathbf { r } ( t ) = t \mathbf { i } + \frac { 25 } { 26 } t ^ { 2 } \mathbf { j } - 8 t \mathbf { k }\)
• E)\(\mathbf { r } ( t ) = t \mathbf { i } - 8 t \mathbf { j } + \frac { 26 } { 25 } t ^ { 2 } \mathbf { k }\)

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