Number of values of c for which set (x,y):x2+y2+2x≤1∩{(x,y):x−y+c≥0} contains only one element

x2+y2+2x≤1⇒x+12+y2≤22   It represents  interior and boundary of the  circle having centre at -1,0 and radius 2since the given two regions have only one point common ⇒the line x - y +c =0 is tangent of the circle.   The perpendicular distance from centre to the line = radius  −1+c2=2⇒c=3;c=−1Reject c=3  (   since  number of common points are infinity ).   If c=−1⇒ number of common points is =1 .