Since, the line (x−2)cosθ+(y−2)sinθ=1 touches a circle. So it is a tangent equation to a circle. Equation of tangent to a circle at (x1,y1) is (x−h)x1+(y−k)y1 =a2 to a circle (x−h)2+(y−k)2=a2 Then, after comparing x−h=x−2y−k=y−2 and a2=1 x1=cosθ,y1=sinθ ∴ Required equation of circle (x−2)2+(y−2)2=1 ⇒x2+y2−4x−4y+7=0
