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Tapasranjan Das Grade: 12
        

Q:-If the distances between the origin and centers of the three circles x2+y2 - 2λr x -a2=0 ; r=1,2,3 are in G.P then the lengths of tangents to the circles from any point on the circle x2+y2=a2 are in__________


1.A.P


2.G.P


3.H.P


4.A.G.P


5.None of these

7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear Tapasranjan


x2+y2 - 2λr x -a2=0


(x-λr)2 +y2 =a2 + λr2


 center of circle( λr,0)


   so distance of center from the origin. = λr


   so λ1 2 ,λare in GP


now let a general point (acos θ ,asinθ) on circle x2+y2=a2    


so length of tangent from this point to the given circle


       = [(acos θ)2+(asinθ)2 - 2λacos θ -a2]1/2


       =[ - 2λacos θ ]1/2


 so given λ1 2 ,λare in GP


   so   -1 acos θ,-2λ2 acos θ,-3 acos θ  will also be in GP


         [ - 2λ1 acos θ ]1/2 , [ - 2λ2 acos θ ]1/2  , [ - 2λ3 acos θ ]1/2  will also be in GP


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Badiuddin



7 years ago
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