1. The problem statement, all variables and given/known data The ellipsoid 4x^2+2y^2+z^2=16 intersects the plane y=2 in an ellipse. Find parametric equations for the tangent line to this ellipse at the point (1,2,2) 2. Relevant equations sin(t)^2 + cos(t)^2 = 1 3. The attempt at a solution After plugging 2 in for y, I get 4x^2 + z^2 = 8 thus x^2/2 + z^2/8 = 1 if sin(t)^2 + cos(t)^2=1 then x^2/2=sin(t)^2 and x = root(2)sint(t) z would = 2root(2)cos(t) and thus the curve of x=root(2)sint(t), y=2, z=2root(2)cos(t) would be the intersect of the plane and the ellipsoid. to get a tangent of the line, it would be r'(t)/|r'(t) at the point x = 1 = root(2)sint(t) -> t = 45degrees meaning that all cos(t) and sin(t) would be root(2)/2 however for r'(t), I get root(2)cos(t)i + 0j + -2root(2)cos(t) and plugging in root(2)/2, will yield a -1. Finding the magnitude of the vector always gets me a root(5) However the answer should be x = 1+t, y=2, z=2-2t am I making this too complicated or do I not get how to parametrize the intersection of a surface and a plane?