Let Γ be the branch x>0 of the hyperbola x2−y2=1. Let P0,P1,...,Pn different points of Γ with P0=(1,0) and P1=(13/12,5/12). Let ti be the tangent line to Γ at Pi. Suppose that for all i≥0 the area of the region bounded by ti,ti+1 and Γ is a constant independent of i. Find the coordinates of the points Pi. CIIMCIIM 2011undergraduate