Find a Vector Function That Represents the Curve of Intersection $x ^ { 2 } + 5 y ^ { 2 } + 5 z ^ { 2 } = 25$

question 136

Multiple Choice

Find a vector function that represents the curve of intersection of the two surfaces:
the top half of the ellipsoid $x ^ { 2 } + 5 y ^ { 2 } + 5 z ^ { 2 } = 25$ and the parabolic cylinder $y = x ^ { 2 }$ .

• A)
• \(\mathrm { r } ( t ) = t \mathbf { i } + t ^ { 2 } \mathbf { j } + \sqrt { \frac { 25 - t ^ { 2 } - 5 t } { 5 } } \mathbf { k }\)
• B) \(\mathbf { r } ( t ) = t \mathbf { i } - t ^ { 2 } \mathbf { j } - \sqrt { \frac { 25 - t ^ { 2 } - 5 t } { 5 } } \mathbf { k }\)
• C)
• \(\mathbf { r } ( t ) = t \mathbf { i } + t ^ { 2 } \mathbf { j } + \sqrt { \frac { 5 - t ^ { 2 } - 5 t ^ { 4 } } { 5 } } \mathbf { k }\)
• D)
• \(\mathbf { r } ( t ) = t \mathbf { i } + t ^ { 4 } \mathbf { j } + \sqrt { \frac { 25 - t ^ { 2 } + 5 t } { 5 } } \mathbf { k }\)
• E)
• \(\mathbf { r } ( t ) = t \mathbf { i } + t ^ { 2 } \mathbf { j } + \sqrt { \frac { 25 + t ^ { 2 } - 5 t ^ { 4 } } { 5 } } \mathbf { k }\)

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