Take home math exam problem (lagrange multiplier)

[splashpot]

Someone want to tell me if I'm missing something with this Lagrange multiplier problem?

Problem: Find the maximum and minimum values of f(x,y)=xy on the curve (x+2)^2 + y^2 =1

This is what I've done-
gradient of f=(y,x)
gradient of g=(2x+4,2y)

According to Lagrange: gradient f = lambda*(gradient g)
So we have the following equations.
y=lambda*(2x+4)
x=lambda*2y
(x+2)^2 + y^2 =1

That's 3 equations and 3 unknowns but I can't seem to find a solution. I feel like I'm missing something really stupid. Or my brain is hitting a wall to solve those equations. Can someone help?

[splashpot]

Nevermind, I got it. Just stupid blank on solving those 3 equations.

[evank15]

Ahhh...Lagrange multipliers.

Really [censored] topic if you suck at solving algebraic systems.

[CityFan]

you could also do it by parametrising the circle (x+2)^2 + y^2 = 1.

x = -2 + cos t
y = sin t

f = sin t cos t - 2 sin t

df/dt = cos t cos t - sin t sin t - 2 cos t
= cos t cos t - (1 - cos t cos t) - 2 cos t
= 2c^2 - 2c - 1 where c = cos t

df/dt = 0
=> 2c^2 - 2c - 1 = 0
=> cos t = [1-sqrt(3)]/2
=> sin t = +/- sqrt[sqrt(3)/2]

f = ...