LaGrange Multipliers.

If you do:

 x^2 + y^2 + λ(blah blah blah)

and differentiate w.r.t x and y you are left with 2 equations:

2x + λ(blah blah blah)
2y + λ(blah blah blah)

where do I go from here?

You also want to differentiate with respect to λ (i.e. formulate the restraints you're given). Set the x, y and λ derivatives to zero, and solve the resulting equations.