QJEEM21Ma4a02: JEE Main 2021 Mathematics - Class 11 JEEM21Ma4a02 Solution: If the equation a

Question

Verified Solution • 2025–26 Session moderate

If the equation

a | z |^{2} + \overset{―}{\overset{―}{α} z + α \overset{―}{z}} + d = 0

represents a circle where a, d are real constants then which of the following condition is correct?

Accepted Answer

a | z |^{2} + α \overset{―}{z} + \overset{―}{α} z + d = 0

\Rightarrow

z \overset{―}{z} + (\frac{α}{a}) \overset{―}{z} + (\frac{\overset{―}{α}}{a}) z + \frac{d}{a} = 0

∴

Centre

= - \frac{α}{a}

r = \sqrt{{| \frac{α}{a} |}^{2} - \frac{d}{a}}

\Rightarrow {| \frac{α}{a} |}^{2} \geq \frac{d}{a}

\Rightarrow {| α |}^{2} \geq a d

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