An Ellipsoid Is Created by Rotating the Ellipse $4 x ^ { 2 } + y ^ { 2 } = 16$

question 58

Multiple Choice

An ellipsoid is created by rotating the ellipse $4 x ^ { 2 } + y ^ { 2 } = 16$ about the x-axis. Find the equation of the ellipsoid.

• A) \(16 x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 1\)
• B) \(4 x ^ { 2 } + y ^ { 2 } - z ^ { 2 } = 16\)
• C) \(4 x ^ { 2 } - y ^ { 2 } + z ^ { 2 } = 16\)
• D) \(4 x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 1\)
• E) \[4 x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 16\]