Consider the hyperbola H: x^2-y^2= 1 and a circle S with center N(x2, 0). Suppose that H and S touch each other at a point P(x1, y1) with x1>1 and y1 > 0. The common tangent to H and S at P intersects the x-axis at point M. If (I, m) is the centroid of the triangle APMN, then the correct expression(s) is(are)