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Show that the line (x – 2) cosθ + (y – 2) sinθ = 1 touches a circle for all values of θ. Find the circle.

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Show that the line (x – 2) cosθ + (y – 2) sinθ = 1 touches a circle for all values of θ. Find the circle.

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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

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