1. The problem statement, all variables and given/known data Find the tangent plane to the surface x2 + 2y2 + 3z2 = 21, which is parallel to the plane x+4y+6z=0 2. Relevant equations Gradients. 3. The attempt at a solution Here is my solution: So gradient of the surface is (2x, 4y, 6z). The normal of the given plane is (1,4,6). Equating both gives us x=0.5, y=1, z=1. So this is the point where the plane meets the surface. Finding the equation: 1(x-0.5)+4(y-1)+6(z-1) = x - 0.5 + 4y - 4 + 6z - 6 Equation for the plane is: x + 4y + 6z = 10.5 The answer given is x + 4y + 6z = ±21. Where did I go wrong? What did I forget to multiply? And why the two solutions (positive and negative)? Thanks!