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-h)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
