JEE PYQ: Complex Numbers Question 6
Question 6 - 2021 (18 Mar Shift 1)
If the equation $a|z|^2 + \bar{\alpha}z + \alpha\bar{z} + d = 0$ represents a circle where $a, d$ are real constants then which of the following condition is correct?
(1) $|\alpha|^2 - ad \neq 0$
(2) $|\alpha|^2 - ad > 0$ and $a \in R - {0}$
(3) $|\alpha|^2 - ad \ge 0$ and $a \in R$
(4) $\alpha = 0, a, d \in R^+$
Show Answer
Answer: (2)
Solution
For the equation to represent a circle: $a \neq 0$ (real), and the radius $\sqrt{\frac{|\alpha|^2}{a^2} - \frac{d}{a}} > 0$, which requires $|\alpha|^2 - ad > 0$.
BETA
