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# Lagrange Multipliers watch

1. Using methods of Lagrange multipliers, find the shortest distance between the ellipse x^2 +3y^2 = 1 and x+3y-3=0. Not sure how to approach this. I understand how to find the distance between a point and a surface/line but not sure how to extend this.
2. (Original post by Palabras)
Using methods of Lagrange multipliers, find the shortest distance between the ellipse x^2 +3y^2 = 1 and x+3y-3=0. Not sure how to approach this. I understand how to find the distance between a point and a surface/line but not sure how to extend this.
I'd imagine that you need to derive and minimise the distance function representing the distance of any point to the line , subject to a constraint that the point must satisfy .

Then once you've found the point at which this distance is minimum (using Lagrange multipliers) just plug it back into your distance formula and you're done.

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Updated: April 14, 2011
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