Complex Numbers: If the equation a|z|^2+baralphaz+alphabarz+d=0 represents a circle… | JEE Main 2021

JEE Main 2021 (Online) 18th March Morning ShiftQuestion 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 ?

Complex Numbers

$|\alpha|^{2}-ad\ge0$ and $a\in\mathbf{R}$$|\alpha|^{2}-ad>0$ and $a\in\mathbf{R}-\{0\}$✓ Correct answer$|\alpha|^{2}-ad\neq0$$\alpha=0$, $a,d\in\mathbf{R}^{+}$

Solution

Divide by $a\ne0$: $|z+\alpha/a|^2=\frac{|\alpha|^2-ad}{a^2}$. A circle (positive radius) needs $a\ne0$ and $|\alpha|^2-ad>0$. Option (B).

Complex Numbers - JEE Mathematics question (JEE Main 2021 (Online) 18th March Morning Shift)

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