find the extremea of f(x,y) = x^2 -4y^2 subject to g(x,y) = x^2+ 4xy +6y^2 =2o.

making use of lagrange multiplier, i got

f(x,y) has a min or max when x^2 +5xy+4y^2 = o and that it has to also fulfil the conditions of g(x,y) = x^2+ 4xy +6y^2 =2o right?

when i solve these 2 equations via simultaneous, i got y=0 and x=2y. then how do i solve the last part?