A) Straight line
B) Circle
C) Parabola
D) None of these
Correct Answer: B
Solution :
\[|z+1|=\sqrt{2}|z-1|\] Putting \[z=x+iy\] Þ \[|x+iy+1|=\sqrt{2}|x+iy-1|\] Þ \[|(x+1)+iy|=\sqrt{2}|(x-1)+iy|\] Þ \[{{(x+1)}^{2}}+{{y}^{2}}=2[{{(x-1)}^{2}}+{{y}^{2}}]\] Þ \[{{x}^{2}}+{{y}^{2}}-6x+1=0\]. Which is the equation of a circle.
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