A) \[\sqrt{\mu -\lambda }\]
B) \[\sqrt{\mu +\lambda }\]
C) \[\sqrt{{{\mu }^{2}}-{{\lambda }^{2}}}\]
D) \[\mu +\lambda \]
E) \[\mu -\lambda \]
Correct Answer: A
Solution :
Let\[({{x}_{1}},{{y}_{1}})\]be the point on the circle \[{{x}^{2}}+{{y}^{2}}+2fy+\lambda =0\] \[\Rightarrow \] \[x_{1}^{2}+y_{1}^{2}+2f{{y}_{1}}+\lambda =0\] \[\Rightarrow \] \[x_{1}^{2}+y_{1}^{2}+2f{{y}_{1}}=-\lambda \] ...(i) Now, the length of tangent from the point \[({{x}_{1}},{{y}_{1}})\]to the circle\[{{x}^{2}}+{{y}^{2}}+2fy+\mu =0\]is \[=\sqrt{(x_{1}^{2}+y_{1}^{2}+2f{{y}_{1}})+\mu }\] \[=\sqrt{\mu -\lambda }\] [from Eq. (i)]
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