Not sure I understand exactly what this question is asking. This is obviously a volume in R3 and so how do you get a tangent inside a volume? Or is it just along the plane y = 2 intersecting the volume? Also, what is a parametric equation...? Thanks for the help: Question: 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). Attempt: I substituted in y = 2 and got the equation 4x^2 + z^2 = 8. Do I just find what the partial derivatives are at the point (1,2)? And would the tangents be combinations of these two derivatives...?