## anonymous one year ago 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?

1. IrishBoy123

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 $$\lambda$$

2. anonymous

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

3. IrishBoy123

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