The range of m for which the line y=mx+2  cuts the circle x2+y2=1  at distinct or coincident point, is

The length of the perpendicular from the centre (0,0)  to the line =2(1+m2). The radius of the circle =1For the line to cut the circle at distinct or coincident points, 2(1+m)2≤1  ⇒ 1+m2≥4   ⇒m2≥3.∴    m∈(−∞,−3]∪[3,+∞)