"If the equation $a|z{|^2} + \overline {\overline \alpha z + \alpha \overline z } + d = 0$ represents a circle where a, d are real constants then which of the following condition is correct?"

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"$a|z{|^2} + \alpha \overline z + \overline \alpha z + d = 0$

$\Rightarrow$ $$z\overline z + \left( {{\alpha \over a}} \right)\overline z + \left( {{{\overline \alpha } \over a}} \right)z + {d \over a} = 0$$

$\therefore$ Centre $= - {\alpha \over a}$

$r = \sqrt {{{\left| {{\alpha \over a}} \right|}^2} - {d \over a}}$

$\Rightarrow {\left| {{\alpha \over a}} \right|^2} \ge {d \over a}$

$\Rightarrow {\left| \alpha \right|^2} \ge ad$"

If the equation $a|z{|^2} + \overline {\overline \alpha z + \alpha \overline z } + d = 0$ represents a circle where a, d are real constants then which of the following condition is correct?

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If the equation $a|z{|^2} + \overline {\overline \alpha z + \alpha \overline z } + d = 0$ represents a circle where a, d are real constants then which of the following condition is correct?

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