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Question

If |z+1|=2|z1|, then locus of z is

A
straight line
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B
circle
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C
ellipse
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D
parabola
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Solution

The correct option is A circle
we have |z+1|=2|z1|
squaring |z+1|2=2|z1|2
Let z=x+iy
(x+1)2+y2=2(x1)2+2y2
x2+2x+y2+1=2x24x+2+2y2
x26x+y2+1=0 is an equation of circle

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