"Find the point on the paraboloid :

z=(x^2)/25 + (y^2)/4

That is closest to the point (0,5,0)"

...my solutions manual solves this using symetry. they say that by symetry we see that x=0. And then the problem turns into a two dimensional problem. and optimize the distance squared... they got (0,2.66,1.76) as the closest point.

...NOW, i did this in 3D using the paraboloid as my constraint, and did it by the method of lagrange multipliers. but i get a totally diff answer were some of my points are negative.

Can someone shed some light please. Thanks in advance