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# Q:- The line (x-1)cosθ  + (y-1)sinθ =1 touches the circle whose equation is_________________ , for all values of θ .

147 Points
11 years ago

Dear Tapasranjan

concept in this question is that length of perpendicular from the center of circle to given line will be constant

not lets center of circle is ( h,k)

so   |(h-1)cosθ +(k-1)sinθ -1|/ √(cos2θ +sin2θ)  = constant

|(h-1)cosθ +(k-1)sinθ -1|   = constant

L H S to be constant only for h=1,k=1

so center will be (1,1)  and radius of the circle = 1

so equation of circle = (x-1)2 + (y-1)2 =1

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