Lagrange multipliers: Variables cancelling out?

[ucbearcat]

Find the maximum and minimum of f(x,y)=y2-x2 with the constraint x2/4 +y2=2.

My calculus professor gave us this on his exam and there were no problems like this in the book and I would just like to know how it's done because it's bothering me ha.

After doing the partial derivatives I got -2x=(x/2)λ and 2y=2yλ. This just makes λ=-4 and 1. I'm not sure what I should have done or do from here since there is no variables to find the min and max unless there is no maximums or minimums but I feel like there would be because it was the only problem about lagrange multipliers on the exam.

 

[hotvette]

Let's look more carefully at your expression involving y:

2y=2yλ

If you rearrange it you can get:

0 = 2yλ-2y = 2y(λ-1)

You've assumed λ-1 = 0. What's the other possibility? Same w/ the equation involving x.

It can also be helpful to recognize that x²/4 +y²=2 is the equation of a common conic.