# Find the point(s) on the surface z^2 = xy + 1 which are closest to the point (7, 5, 0

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• April 28th 2010, 04:39 PM
ewkimchi
Find the point(s) on the surface z^2 = xy + 1 which are closest to the point (7, 5, 0
Find the point(s) on the surface http://webwork.math.ucdavis.edu/webw...8a9f0e2301.png which are closest to the point (7, 5, 0).

List points as a comma-separated list, (e.g., (1,1,-1), (2, 0, -1), (2,0, 3)).
• April 28th 2010, 08:59 PM
mr fantastic
Quote:

Originally Posted by ewkimchi
Find the point(s) on the surface http://webwork.math.ucdavis.edu/webw...8a9f0e2301.png which are closest to the point (7, 5, 0).

List points as a comma-separated list, (e.g., (1,1,-1), (2, 0, -1), (2,0, 3)).

Minimise $D^2 = (x - 7)^2 + (y - 5)^2 + z^2$ subject to the constraint $z^2 = xy + 1$.

Please show your work and say where you get stuck if you need more help.