If the equation $a | z | ^ { 2 } + \overline { \bar { \alpha } z + \alpha \bar { z } } + d = 0$ represents a circle where $a , d$ are real constants then which of the following condition is correct?\\
(1) $| \alpha | ^ { 2 } - a d \neq 0$\\
(2) $| \alpha | ^ { 2 } - a d > 0$ and $a \in R - \{ 0 \}$\\
(3) $| \alpha | ^ { 2 } - a d \geq 0$ and $a \in R$\\
(4) $\alpha = 0 , a , d \in R ^ { + }$