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**superdude** the surface $\displaystyle 6x^2+3y^2+3z^2-6yz-2y-2z=0$ has one horizontal tangent plane. Find its equation and give the point where it is tangent.

Hint(?) there is no piont on the surface below this plane

I've taken the partial derivatives and got $\displaystyle \frac{dz}{dx}=\frac{-12x^2}{6z-6y-2}$ and $\displaystyle \frac{dz}{dy}=\frac{-6y-2}{6z-6y-2}$. I'm not sure what to do next since I can't equate them with 0 and solve for a variable.

I haven't learned about vectors yet