The distance between some point 
and the origin is given by
so this is the function we're trying to minimize. But notice that
and 
attain their critical points at the same , so we can solve the same problem by minimizing 
instead.
So let's take the Lagrangian to be
with partial derivatives (set equal to 0)
Now, notice that
and we can use this to solve for
. We get
At this critical point, we get a minimum distance of
so this is the function we're trying to minimize. But notice that
So let's take the Lagrangian to be
with partial derivatives (set equal to 0)
Now, notice that
and we can use this to solve for
At this critical point, we get a minimum distance of