A) 3
B) 4
C) 5
D) 6
Correct Answer: C
Solution :
Let \[z=x+iy\] \[\therefore \,\,\left| \frac{z-25}{z-1} \right|=5\] \[\Rightarrow \] \[\left| \frac{(x-25)+iy}{(x-1)+iy} \right|=5\] \[\Rightarrow \] \[\left| (x-25)+iy\, \right|=5|(x-1)+iy|\] \[\Rightarrow \] \[\sqrt{(x-{{25}^{2}}+{{y}^{2}}}=5\sqrt{{{(x-1)}^{2}}+{{y}^{2}}}\] On squaring both sides, we get \[{{(x-25)}^{2}}+{{y}^{2}}=25\,\{{{(x-1)}^{2}}+{{y}^{2}}\}\] \[\Rightarrow \]\[{{x}^{2}}-50x+625+{{y}^{2}}\] \[=25{{x}^{2}}-50x+25+25{{y}^{2}}\] \[\Rightarrow \]\[24{{x}^{2}}+24{{y}^{2}}=600\] \[\Rightarrow \]\[{{x}^{2}}+{{y}^{2}}=25\] \[\Rightarrow \]\[\sqrt{{{x}^{2}}+{{y}^{2}}}=5\] [\[\because \]\[\left| \,z\, \right|=\sqrt{({{x}^{2}}+{{y}^{2}})}\]] \[\Rightarrow \] \[\left| \,z\, \right|=5\]
You need to login to perform this action.
You will be redirected in
3 sec
