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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 .

6 years ago


Answers : (1)


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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6 years ago

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