Find the Point(s) on the Hyperboloid $x ^ { 2 } + 4 y ^ { 2 } + z ^ { 2 } = 84 \text { where the tangent plane is }$

question 8

Multiple Choice

Find the point(s) on the hyperboloid $x ^ { 2 } + 4 y ^ { 2 } + z ^ { 2 } = 84 \text { where the tangent plane is }$ perpendicular to the line with parametric equations $x = 5 - 8 t , y = 1 + 32 t , \text { and } z = 2 - 4 t$

• A) \(( - 4 , - 4 , - 2 ) , ( 4,4,2 )\)
• B) \(( - 4,4,2 )\)
• C) \(( 4 , - 2 , - 2 )\)
• D) \(( 4 , - 4 , - 2 ) , ( 4,4,2 )\)
• E) \(( - 4,4 , - 2 ) , ( 4 , - 4,2 )\)

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