Surface level of a curve, does it influence the tangent plane?

[jenuine]

Homework Statement

Does the surface level of a curve influence the tangent plane of that curve? If so, how do I find the tangent plane specific to that level?

 

[Mark44]

What do you mean, "surface level of a curve"?

 

[jenuine]

Well for instance f(x,y,z)=xy+xz+xyz. Then the level surface f=10 would be xy+xz+xyz=10. I am just wondering whether this level surface will influence the equation of the tangent plane. If so, how do I find it with respect to that level surface.