The set of values of 'c' so that the equations y=|x|+c and x2+y2−8|x|−9=0 have no solution is
5√2−4,∞
Since y=|x|+c and x2+y2−8|x|−9=0 both are symmetrically about y-axis for x>0, y=x+c.
Equation of tangent to circle x2+y2−8x−9=0 parallel to y=x+c is y=(x−4)+5√1+1
⇒y=x+(5√2−4)
For no solution c>5√2−4
∴cϵ(5√2−4,∞)