Complex Numbers And Quadratic Equations question 355
Question: If $ |z+1|=\sqrt{2}|z-1|, $ then the locus described by the point $ z $ in the Argand diagram is a
Options:
A) Straight line
B) Circle
C) Parabola
D) None of these
Show Answer
Answer:
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.
BETA
