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**renjer****Member**- Registered: 2006-04-29
- Posts: 51

Use Lagrange multipliers to find the minimum distance from the point (5,5,4) to the paraboloid z=4-x^2-y^2.

I know a lot about Lagrange multipliers, they're quite easy, but the problem is, how do you find the distance from a point in space to a surface?

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 13,488

I don't know about Lagrange multipliers and read about it here.

If your problem requires finding the distance between a point and a surface, the distance required must be the shortest distance to the point from normal to the surface!

Character is who you are when no one is looking.

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**renjer****Member**- Registered: 2006-04-29
- Posts: 51

Then how can I relate that to Lagrange multipliers? I know there is supposed to be 2 equations f(x,y,z) and g(x,y,z) but now I don't know which two equations can I use.

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,306

you can set up a distance function,

maximize it or its square under the constraint z=4-x^2-y^2.

**X'(y-Xβ)=0**

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