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

Short Answer

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 $y = x ^ { 2 }$ .