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March 25th, 2017, 05:16 PM   #1
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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.
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March 25th, 2017, 05:34 PM   #2
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Originally Posted by zollen View Post
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
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March 25th, 2017, 05:48 PM   #3
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https://en.wikipedia.org/wiki/Lagrange_multiplier

above is general method or this type of problem
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March 25th, 2017, 06:56 PM   #4
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Originally Posted by mathman View Post
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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