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Q.

The equation zz¯+az¯+a¯z+b=0, b∈R  represents a circle(not point circle) if:

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a

|a|2>b

b

|a|2

c

|a|>b

d

|a|

answer is A.

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Detailed Solution

zz¯+az¯+a¯z+b=0 ⇒ zz¯+az¯+a¯z+aa¯=aa¯−b ⇒(z+a)(z¯+a¯)=aa¯−b ⇒ |z+a|2=|a|2−b This represents a circle (not point circle) if |a|2>b
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The equation zz¯+az¯+a¯z+b=0, b∈R  represents a circle(not point circle) if: