A) an ellipse
B) a circle
C) a straight line
D) None of the above
Correct Answer: C
Solution :
Given, \[\left| z-3 \right|=\left| z-5 \right|\] On squaring both sides, we get \[(z-3)(\overline{z}-3)=(z-5)(\overline{z}-5)\] \[\Rightarrow \] \[z\overline{z}-3\overline{z}-3z+9=z\overline{z}-5\overline{z}-5z+25\] \[\Rightarrow \] \[2\overline{z}+2z=16\Rightarrow z+\overline{z}=8\] \[\Rightarrow \] \[2x=8\Rightarrow x=4\] (putting\[z=x+iy\]) Hence, locus of\[z\]is a straight line parallel to y-axis.
You need to login to perform this action.
You will be redirected in
3 sec
