# Lagrange Multiplier Question

Gold Member

## Homework Statement

f(x,y) = y2-x2, g(x,y) = x2/4 +y2=9

## Homework Equations

$\nabla f = \lambda \nabla g$

$-2x = \lambda \frac{x}{2}$
$2y = 2\lambda y$
$\frac{1}{4} x^2 + y^2 = 9$

## 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?

Dick
Homework Helper
−2x=λx/2 means EITHER λ=(-4) OR x=0. You have to check both options.

Ray Vickson
Homework Helper
Dearly Missed

## Homework Statement

f(x,y) = y2-x2, g(x,y) = x2/4 +y2=9

## Homework Equations

$\nabla f = \lambda \nabla g$

$-2x = \lambda \frac{x}{2}$
$2y = 2\lambda y$
$\frac{1}{4} x^2 + y^2 = 9$

## 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?

If x ± 0 then λ = -4, so in the second equation you must have y = 0.

RGV

Last edited:
Dick
Homework Helper

If x ± 0 then λ = 4, so in the second equation you must have y = 0.

RGV

Ray Vickson
Homework Helper
Dearly Missed

I had the typo λ = 4 instead of the correct λ = -4, but that still implies we need y = 0 to satisfy the second equation (which would be 2y = -8y).

RGV

Gold Member
Ok, well a lambda of -4 makes the other equation untrue. So lambda can not be -4 then, right?

Dick