Find an equation of the tangent plane to the surface $$ x^{2}+6 y^{2}+z^{2}=891 $$ at the point $$ (9,-9,18) $$.

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1. Define the function representing the surface:
   $$
   f(x,y,z) = x^2 + 6y^2 + z^2.
   $$
   The surface is given by $$ f(x,y,z) = 891 $$.
   
2. Compute the gradient of $$ f $$:
   $$
   \nabla f(x,y,z) = \left( \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z} \right) = \left( 2x,\, 12y,\, 2z \right).
   $$
   
3. Evaluate the gradient at the point $$ (9,-9,18) $$:
   $$
   \nabla f(9,-9,18) = \left( 2(9),\, 12(-9),\, 2(18) \right) = \left( 18,\, -108,\, 36 \right).
   $$
   
4. The equation of the tangent plane at $$ (9,-9,18) $$ is given by the dot product formula:
   $$
   \nabla f(9,-9,18) \cdot \left( x-9,\, y+9,\, z-18 \right) = 0.
   $$
   Substituting the gradient, we have:
   $$
   18 (x-9) - 108 (y+9) + 36 (z-18) = 0.
   $$
   
5. Simplify the equation. Divide the entire equation by $$ 18 $$:
   $$
   (x-9) - 6 (y+9) + 2 (z-18) = 0.
   $$
   Expanding the terms:
   $$
   x - 9 - 6y - 54 + 2z - 36 = 0.
   $$
   Combine like terms:
   $$
   x - 6y + 2z - 99 = 0.
   $$
   
6. Rearranging, the equation of the tangent plane is:
   $$
   x - 6y + 2z = 99.
   $$
The equation of the tangent plane to the surface $$ x^{2} + 6y^{2} + z^{2} = 891 $$ at the point $$ (9, -9, 18) $$ is: $$ x - 6y + 2z = 99. $$

Find an equation of the tangent plane to the surface at the point .

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