# Math Help - setting up this equation (two variable one constraint)

1. ## setting up this equation (two variable one constraint)

Find the max and min distance from the origin to the ellipse x^2+xy+y^2=3
Use x^2+y^2 as your objective function.

I tried to do this by using x^2+xy+y^2=3 as my constraint but it doesn't give me the right answer. I can't check the qualification of the constraint because there is an X and a Y when I take partial deriviative of that function. I don't know what to do..

thanks alot

2. Originally Posted by s0urgrapes
Find the max and min distance from the origin to the ellipse x^2+xy+y^2=3
Use x^2+y^2 as your objective function.

I tried to do this by using x^2+xy+y^2=3 as my constraint but it doesn't give me the right answer. I can't check the qualification of the constraint because there is an X and a Y when I take partial deriviative of that function. I don't know what to do..

thanks alot

$L(x,y,\lambda)=x^2+y^2+\lambda(x^2+xy+y^2-3)$

So now what is the problem?

CB

3. Originally Posted by CaptainBlack

$L(x,y,\lambda)=x^2+y^2+\lambda(x^2+xy+y^2-3)$

So now what is the problem?

CB
So to find the max and min of the function, I take the partial derivatives with respect to X, Y and lambda, then what? I get stuck after that

Thanks!

4. Originally Posted by s0urgrapes
So to find the max and min of the function, I take the partial derivatives with respect to X, Y and lambda, then what? I get stuck after that

Thanks!
Equate the partial derivatives to zero and solve the resulting system of simultaneous equations.

5. ok i got that, thanks!

now theyre asking me to check the second order conditions for those partial derivatives..

how do i do that?