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 March 25th, 2017, 05:16 PM #1 Senior Member   Joined: Jan 2017 From: Toronto Posts: 178 Thanks: 2 Shortest distance to the origin Find all points on the surface xy - z^2 + 1 = 0 that are closest to the origin. Answer: (0, 0, 1) and (0, 0, -1) Any tips would be much appreciated.
March 25th, 2017, 05:34 PM   #2
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Quote:
 Originally Posted by zollen Find all points on the surface xy - z^2 + 1 = 0 that are closest to the origin. Answer: (0, 0, 1) and (0, 0, -1) Any tips would be much appreciated.
I'm going to give you an overview.

First find the distance from a point (the origin) to some place on the curve. You'll have to solve your equation for z to do this. Then you minimize the distance expression.

-Dan

 March 25th, 2017, 05:48 PM #3 Global Moderator   Joined: May 2007 Posts: 6,524 Thanks: 588 https://en.wikipedia.org/wiki/Lagrange_multiplier above is general method or this type of problem
March 25th, 2017, 06:56 PM   #4
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Quote:
 Originally Posted by mathman https://en.wikipedia.org/wiki/Lagrange_multiplier above is general method or this type of problem
"Lagrange multipliers?" That's sooo 1880's.

-dan

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