Gradient of curve? (Langrangian multipliers)

[Pelleman]

I dont understand the usage of the word gradient often used in the explanation of lagrangian multipliers.
Say you seek the maximum of some function f(x,y) given the constraint G(): x^2+y^2 = 3.
since the constrant is just a curve how could one get "gradient" of it. Sounds a bit irregular...
I understand the rest of the idea, just not the "gradient" of a curve.

 

[Romsek]

you take the gradient of [MATH]f(x,y) - \lambda (g(x,y)-C)[/MATH]
where \(\displaystyle C\) is what your constraint function is constrained to equal and \(\displaystyle \lambda\) is the Lagrange multiplier.

The gradient is taken with respect to \(\displaystyle (x,y,\lambda)\) and the the result of differentiating w/respect to \(\displaystyle \lambda\)
just gets you the constraint term of the original problem.