Question

The equation $z\overline{z}+(4-3i)z+(4+3i)\overline{z}+5=0$ represents a circle whose radius is

• A. 5
• B. 2$\sqrt{5}$
• C. $\frac{5}{2}$
• D. none of these

Answer 1

Answer: (B)

2$\sqrt{5}$

$z\overline{z}+(4-3i)z+(4+3i)\overline{z}+5=0$ represents a circle.
Let $z=x+iy$
$\Rightarrow (x+iy)(x-iy)+(4-3i)(x+iy)+(4+3i)(x-iy)+5=0$
$\Rightarrow x^2+y^2+4x+4iy-3ix+3y+4x-4iy+3ix+3y+5=0$
$\Rightarrow x^2+y^2+8x+6y+5=0$
Radius $r=\sqrt{16+9-5}=\sqrt{20}=2\sqrt{5}$
Hence, option B.