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A circle `x^2+y^2+4x-2sqrt(2)y+c=0`is the director circle of the circle `S_1a n dS_1`is the director circle of circle `S_2,`and so on. If the sum of radii of all these circles is 2, then thevalue of `c`is `ksqrt(2)`, where the value of `k`is___________ |
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Answer» Correct Answer - 4 The radius of the given circle `x^(2)+y^(2)+4x-2sqrt(2)y+c=0` is `ssqrt(4+2-c) = sqrt(6-c)=a` (let). Now, radius of circle `S_(1)=(a)/(sqrt(2))` Radius of circle `S_(2)=(a)/(2)` and so on . Also, `a +(a)/(sqrt(2))+(a)/(2)+ .......+oo=2` (Given ) Then `a((1)/(1-1//sqrt(2)))=2` or `(asqrt(2))/(sqrt(2)-1)=2` or `a=2-sqrt(2)=sqrt(6-c)` or `4+2-4sqrt(2)=6-c` or `c=4 sqrt(2)` |
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