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Question

The equation z¯z+a¯z+¯az+b=0,b ϵ R represents a circle if

A
|a|2=b
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B
|a|2>b
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C
|a|2<b
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D
None of these
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Solution

The correct option is B |a|2>b
By adding a¯a on both the sides of z¯z+a¯z+¯az=b
we get, (z+a)(¯z+¯a)=a¯ab
|z+a|2=|a|2b, z¯z=|z|2
This equation will represent a circle with centre z=a,if|a|2b>0,i.e.|a|2>b since |a|2=b represents point circle only.

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