Can someone help me on the following Lagrange multiplier problems:

1.) Find the points of the parabola y = (x-1)^2 that are closest to the origin.

2.) Find the first-quadrant point of the curve xy=24 that is closest to the point (1,4)

3.) Find teh points on teh sphere with center (1,2,3) and radius 6 that are closest to and farthest from the origin