If the equation a|z|^2 + bar (bar α z + α bar z) + d = 0 represents a circle

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) |α|²- ad ≠ 0

(2) |α|² - ad > 0 and a ∈ R - {0}

(3) |α|² - ad ≥ 0 and a ∈ R

(4) α = 0, a, d∈ R⁺

Answer 1

Have a look in image for answer