Find the points on the surface closest to the origin

[EgyptMind]

1. Homework Statement
find the points on the surface z^2=xy+4 closest to the origin

i tried the distance formula but it got too messy, i think there's an approach using lagrange multiplier but i just can't quiet figure it out...?

 

[lanedance]

to use lagrange, write the function you are trying to minimise (distance to origin r^2 = x^2 + y^2 + z^2), and use the surface as the constraint

 

[EgyptMind]

a little more details...?

 

[lanedance]

what have you tried? post #2 outlines a method to attempt

 

[lanedance]

if you;re not sure about lagrange multipliers, try a google search, i found
http://www.uAlberta.ca/MATH/gauss/fcm/calculus/multvrbl/basic/Extrema/Lgrng_mltplrs_exmpl.htm

 

[HallsofIvy]

1. Homework Statement
find the points on the surface z^2=xy+4 closest to the origin

i tried the distance formula but it got too messy, i think there's an approach using lagrange multiplier but i just can't quiet figure it out...?

What did you try? If you use lanedance's suggestion, to minimize $x^2+ y^2+ z^2$ rather than $\sqrt{x^2+ y^2+ z^2}$ (whatever minimizes one minimizes the other) it should not be "too messy".