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If the equation \(a{\left|z\right|}^{2}+\overset{¯}{\overset{¯}{\alpha }z+\alpha \overset{¯}{z}}+d=0\) represents a circ…

Q1

If the equation \(a{\left|z\right|}^{2}+\overset{¯}{\overset{¯}{\alpha }z+\alpha \overset{¯}{z}}+d=0\) represents a circle where \(a, d\) are real constants, then which of the following condition is correct?

[JEE Main 2021, 18 Mar (Shift 1)]

a

\(|\alpha|^2-a d \neq 0\)

b

\(\alpha=0, a, d \in R^{+}\)

c

\(|\alpha|^2-a d \geq 0\) and \(a \in R\)

d

\(|\alpha|^2-a d>0\) and \(a \in R-\{0\}\)

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