Help with Grobner Basis in Mupad

Hi In a lagrange multipliers problem i'm trying to eliminate lamda out of the equation. I was trying to do it by grobner basis in Mupad but it isn't really working. Can some one give me a bit help how should it be done?

J:=x^2+y^2

e1:=6*x+6*y +2*x*y+1+k

e2:=(x-1)^2+(y-1)^2-k

C:=e1*e2;

L:=J+lamda*C

Lx:=diff(L,x)

Ly:=diff(L,y)

Llamda:=C

This is what I'm getting [lamda^2, 4*k*lamda - y - 5*lamda, k^2 - k + 108*lamda - 24*y - 2, lamda*y, y - 27*lamda + 4*k*y, y^2, x - y]

I would like my basis to be a variable of J (J=x^2+y^2)and k. How can it be done?

Thanks

Nachum