- #1

ElijahRockers

Gold Member

- 270

- 10

## Homework Statement

f(x,y) = y

^{2}-x

^{2}, g(x,y) = x

^{2}/4 +y

^{2}=9

## Homework Equations

[itex]\nabla f = \lambda \nabla g[/itex]

[itex]-2x = \lambda \frac{x}{2}[/itex]

[itex]2y = 2\lambda y[/itex]

[itex]\frac{1}{4} x^2 + y^2 = 9[/itex]

## The Attempt at a Solution

I arrived at the three equations above. So according to the first equation, lambda can equal -4. According to the second equation, it can equal 1. After this, I am algebraically lost. The x's and y's cancel themselves out from the first two equations. What does this mean?