Use "Lagranges" multiplication method to find points in the curve; 5x^2 + 6xy + 5y^2 = 1, which is closest and furtherest away from origo - and find the max/min distance.

What would be the steps involved solving this?

Question

Use "Lagranges" multiplication method to find points in the curve; 5x^2 + 6xy + 5y^2 = 1, which is closest and furtherest away from origo - and find the max/min distance.

What would be the steps involved solving this?

irishboy123 · Answer

you are minimising a function - the distance formula - which we shall call f(x,y) with this ellipse as the condition g(x,y) 

the lagrange multiplier reduces the algebra down to solving this: $\nabla f = \lambda \nabla g$  ie solve for $\lambda$

anonymous · Answer

Okay, It looks like I will have to do some more work on gradients - as I am not very familiar with those

irishboy123 · Answer

well, that's just shorthand for $\large \frac{\partial f}{\partial x} = \lambda\frac{\partial g}{\partial x}$ and $\large \frac{\partial f}{\partial y} = \lambda\frac{\partial g}{\partial y}$