JEE Math Practice Question

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?

1. A.|$$\alpha$$|2 $$-$$ ad $$\ne$$ 0
2. B.|$$\alpha$$|2 $$-$$ ad > 0 and a$$\in$$R $$-$$ {0}
3. C.|$$\alpha$$|2 $$-$$ ad $$ \ge $$ 0 and a$$\in$$R
4. D.$$\alpha$$ = 0, a, d$$\in$$R+