Since the line (x – 2) cosθ + (y – 2) sinθ = 1 .......(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 – y)2+ (y – k)2= a2 comparing (1) and (2) we get
x – h = x – 2 y – k = y – 2 and a2 = 1
x1 = 1cosθ y1 = 1sinθ
∴ Required equation of circle is
(x – 2)2 + (y – 2)2 = 1
x2 + y2– 4x – 4y + 7 = 0
