So, it is given that -
The tangent plane to the ellipsoid $4x^2 + y^2 + 2z^2 = 16$ is $2x + y + 2z = k$.
I’m trying to find k, and the point of tangency between those two.
What I did - Assumed that the normal to the plane is parallel to the gradient of the ellipsoid, so I get $(8x, 2y, 4z) = (2, 1, 2)$. But then I get point $(x, y, z)$ which isn’t on the ellipsoid.
Why is my assumption wrong?