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Question

If z=32+cosθ+isinθ, then locus of z is

A
x2+y2+4x+3=0
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B
x2+y2+4x3=0
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C
x2+y24x3=0
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D
x2+y24x+3=0
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Solution

The correct option is D x2+y24x+3=0
Given : z=32+cosθ+isinθ
3z=2+cosθ+isinθcosθ+isinθ=3z2
Taking mod on both sides, we get
1=|32z||z||z|=|32z|x2+y2=(32x)2+4y23x2+3y212x+9=0x2+y24x+3=0

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