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Lagrange Multipliers - quick help!

The question is:

Use lagrange method to find max and min lengths of the radius vectors contained in the ellipse 5(x^2) + 6xy + 5(y^2) = 8

I know use the form F = f + ?g

but I don't quite know what to use as my f? I know that g is 5(x^2) + 6xy + 5(y^2) - 8 = 0.

All input is much appreciated, thanks :smile:
Reply 1
A radius vector is just the distance from the centre of the ellipse to a point on the periphery of the ellipse.

Call this distance f. Then f=x2+y2f=\sqrt{x^2+y^2} where the point (x,y) satisfies the ellipse 5x2+6xy+5y2=85x^2+6xy+5y^2=8

So, f is the function that you want to minimise/maximise and g is the constraint on it.

F=f+λgF=f +\lambda g

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