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Math Help - find horizontal tangent plane

  1. #1
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    find horizontal tangent plane

    the surface 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 \frac{dz}{dx}=\frac{-12x^2}{6z-6y-2} and \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
    Last edited by superdude; October 11th 2009 at 08:43 PM. Reason: added last line
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  2. #2
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    Quote Originally Posted by superdude View Post
    the surface 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 \frac{dz}{dx}=\frac{-12x^2}{6z-6y-2} and \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
    Yes, you can. A horizontal plane must be of the form z= constant. Set the partial derivatives with respect to x and y equal to 0 and find the correct point of tangency.
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  3. #3
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    I am unclear how to proceed. You want me to treat z as a constant but how do I know what to set it to?

    12x^2+6\frac{dz}{dx}-6y\frac{dz}{dx}=0 and 6y+6\frac{dz}{dy}=6y\frac{dz}{dy}-2-2\frac{dz}{dy}=0
    Last edited by superdude; October 12th 2009 at 04:53 PM.
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