Let C be the intersection of the two surfaces:
S1: x^2 + 4y^2 + z^2 = 6;
s2: z = x^2 + 2y;
Show that the point (1, -1, -1) is on the curve C and find the tangent line to the curve C at the point (1, -1, -1).
partial derivates, maybe the gradient vector and directional derivatives
though, maybe symmetrical equations like x - x_0/partial derivative with respect to x = y etc...
The Attempt at a Solution
I'm just kind of wondering where to start. I think I should be making these into vectors, but I'm not quite sure how to do so, and of course thinking about partial derivatives.