Solving Minimization Problem w/ Lagrange Multipliers

[numberthree]

Homework Statement

Solve the following problems using Lagrange multipliers
(a) Minimise J (x; y) = x^2 + y^2 subject to C (x; y) = 4x^2 + 3y^2 = 12:

Homework Equations

The Attempt at a Solution

i got h(x,y)=x^2+y^2+$$\lambda$$(4x^2+3y^2-12)

dh/dx=2x+8x$$\lambda$$=0
dh/dy=2y+6y$$\lambda$$=0

then i got $$\lambda$$=-1/4=-1/3?impossible to slove it

 

[hotvette]

The values you obtained for $$\lambda$$ made an assumption that neither x or y are zero. Can you really make that claim? Also, maybe there is more than one solution (i.e. a min and a max)? Might help to draw a picture.