Question

The equation $z\overline{z}+a\overline{z}+\overline{a}z+b$ = 0, b$\in$R represents a circle if

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is B

By adding $a\overline{a}$ on both the sides of $z\overline{z}+a\overline{z}+\overline{a}z$ = -b

We get, $(z+a)$$\overline{z}+\overline{a}$ = $a\overline{a}-b$

$\Rightarrow |z+a{|}^2$ = $|a{|}^2-b$, {$\because z\overline{z}$ = $|z{|}^2$ }

This equation will represent a circle with centre

z = -a, if $|a{|}^2-b>0$,i.e.$|a{|}^2>b$ since $|a{|}^2$ = b

represents point circle only.