Find the distance from the origin to the closest point(s) on the graph of [math]

We begin by computing [math] implicitly for points [math] on the graph, obtaining:
[math]
We need to minimize the following function of [math] and [math]:
[math]
There are four critical points, in increasing order:
[math]
[math]
[math]
[math]
Thus there is/are point(s) closest to the origin, one of which is
[math] [math] [math]
and its distance from the origin is