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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?

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  1. IrishBoy123
    • one year ago
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    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
    • one year ago
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    Okay, It looks like I will have to do some more work on gradients - as I am not very familiar with those

  3. IrishBoy123
    • one year ago
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    well, that's just shorthand for \(\large \frac{\partial f}{\partial x} = \lambda\frac{\partial g}{\partial x}\) and \(\large \frac{\partial f}{\partial y} = \lambda\frac{\partial g}{\partial y}\)

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