Find a Parametric Representation for the Part of the Elliptic $x + y ^ { 2 } + 10 z ^ { 2 } = 5$

question 58

Multiple Choice

Find a parametric representation for the part of the elliptic paraboloid $x + y ^ { 2 } + 10 z ^ { 2 } = 5$ that lies in front of the plane $x = 0$ .

• A) \(x = x , y = \sqrt { 5 - x - 10 z ^ { 2 } } , z = z\)
• B) \(x = 5 - y ^ { 2 } - 10 z ^ { 2 } , y = y , z = y , y ^ { 2 } + 10 z ^ { 2 } \leq 5\)
• C) \(x = 5 - y ^ { 2 } - 10 z ^ { 2 } , y = y , z = y , 0 \leq y ^ { 2 } + 10 z ^ { 2 } \leq 3\)
• D) \(x = x , y = \pm \sqrt { 5 - x - 10 z ^ { 2 } } , z = z\)
• E) \(x = 5 - y ^ { 2 } - 10 z ^ { 2 } , y = y , z = y , y ^ { 2 } + 10 z ^ { 2 } \geq 5\)

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