finding max/min with Lagrange Multipliers

Find the extreme values of *f* on the region described by the inequality. *f*(*x*,*y*) = 2*x*^2 + 3*y^*2 - 4*x* -9, *x^*2 + *y^*2 ≤ 16

I am very confused with the steps of how to approach these types of problems. I found..

-partial deriv of x: 4x-4

-partial deriv of y: 6y

Then, I followed an example in my book and found the critical point by setting those equations above to 0, getting x=1, y=0; so the point would be (1,0)

Then, use Lagrange multipliers like this

<4x-4, 6y>=**λ**(2x,2y)...

4x-4=**λ**2x

6y=**λ**2y

Here's where I get a little lost because I'm not really sure what to solve for (x,y, or **λ**?) and where/what I plug that into when I find it... I tried solving 6y=**λ**2y, getting **λ **= 3, then plugging it into x=4/4-2**λ**, but I don't think that's right.

Thank you so much for your help!