A) \[\frac{13}{12}\]
B) \[\frac{5}{12}\]
C) 5
D) 625
Correct Answer: B
Solution :
Key idea: \[\left| \frac{z-\alpha }{z-\beta } \right|=k\] ...(i) where\[\alpha \]and\[\beta \]are constant complex numbers represents circle, if\[k\ne 1\]and its radius is \[\left| \frac{k(\alpha -\beta )}{1-{{k}^{2}}} \right|\] ??(i) Given \[\left| \frac{z-i}{z-(i)} \right|=5\] \[\therefore \] \[\alpha =i\beta =-i,k=5\] [by comparing with Eq. (i)] \[\therefore \]Radius\[=\left| \frac{5(i+i)}{1-25} \right|\] \[=\frac{5}{12}\] Note: \[\left| \frac{z-\alpha }{z-\beta } \right|=k\]for\[k=1\]represents a straight line.
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