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## Homework Statement

Find the tangent plane to the surface x

^{2}+ 2y

^{2}+ 3z

^{2}= 21, which is parallel to the plane x+4y+6z=0

## Homework Equations

Gradients.

## 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!