Question

Find the equation of a circle whose centre is $z_1$ and radius r.

• A. z - - + + = 0
• B. z - z - + - = 0
• C. z + z + + + = 0
• D. z - z - + - = 0

Answer 1

The correct option is B

z - z - + - = 0

$|$z - $z_1$ $|$ = r

$\Rightarrow$ (z - $z_1$) $\left(\overline{z-z_1}\right)$ = $r^2$
$(z-z_1)$($\overline{z}-{\overline{z}}_1$) = $r^2$
$\Rightarrow$ z$\overline{z}$ - z${\overline{z}}_1$ - $z_1$$\overline{z}$ + $z_1$${\overline{z}}_1$ = $r^2$
$\Rightarrow$ z$\overline{z}$ - ${\overline{z}}_1$z - $z_1$$\overline{z}$ + $z_1$${\overline{z}}_1$ - $r^2$ = 0