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Question

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


A

|a|2 = b

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B

None of these

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C

|a|2 < b

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D

|a|2 > b

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Solution

The correct option is D

|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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