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Q.

If the equation a|z|2+α¯z+αz¯¯+d=0 represents a circle, where a, d are real constants, Then which of the following is true

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a

|α|2-ad>0 and a∈R-{0}

b

|α|2-ad≥0 and a∈R

c

α=0,a,d∈R+∣

d

|α|2-ad≠0

answer is A.

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Detailed Solution

a|z|2+αz¯+α¯z+d=0|z|2+αaz¯+α¯az+da=0 Centre =-αar=αa2-da∣|α|2a2-da>0 |α|2-ad>0 &a∈R-{0}
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