Find the tangent plane to the surface x2 + 2y2 + 3z2 = 21, which is parallel to the plane x+4y+6z=0
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)?