Find an Equation of the Tangent Plane to the Hyperboloid $x ^ { 2 } + y ^ { 2 } - z ^ { 2 } - 2 x y + 4 x z = 4$

question 150

Multiple Choice

Find an equation of the tangent plane to the hyperboloid $x ^ { 2 } + y ^ { 2 } - z ^ { 2 } - 2 x y + 4 x z = 4$ at the point $( 1,0,1 )$ .

• A) \(3 x - y + z = 4\)
• B) \(2 x - 4 y + z = 3\)
• C) \(x + 2 y + 3 z = 4\)
• D) \(2 x + y - z = 1\)
• E) \(3 x + 2 y - z = 2\)
• F) \(4 x - y + 2 z = 6\)
• G) \(x + y - z = 0\)
• H) \(5 x + 3 y - 2 z = 3\)