Hyperbola

Consider the hyperbola H:x2−y2=1 and a circle S with center N(x2,0).Suppose that H and S touch each other at a point P(x_1,y_1) with x1>1 and y1>0.The common tangent to H and S at P intersects the x-axis at point M.If (l,m) is the centroid of the triangle ∆PMN,then the correct expression(s) is (are)