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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 .`
7 years ago

147 Points
```										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
Please feel free to post as many doubts on our discussion forum as you can.If you find any question Difficult to understand - post it here and we will get you the answer and detailed  solution very  quickly. We are all IITians and here to help you in your IIT JEE preparation.All the best. Regards,Askiitians ExpertsBadiuddin

```
7 years ago
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