Question

$z\overline{z}+(3-i)z+(3+i)\overline{z}+1=0$ represents a circle with

• A. Centre (-3, -1) and radius 3
• B. Centre (-3, 1) and radius 3
• C. Centre (-3, -1) and radius 4
• D. Centre (-3, 1) and radius 4

Answer 1

Answer: (A)

Centre (-3, -1) and radius 3

Given equation:

$z\overline{z}+(3-i)z+(3+i)\overline{z}+1=0$

Let $z=x+iy$ then $\overline{z}=x-iy$

$z\overline{z}+(3-i)z+(3+i)\overline{z}+1=0$

$(x^2+y^2)+3x+3iy-ix+y+3x-3iy+ix+y+1=0$

$x^2+y^2+6x+2y+1=0$

Centre:$(-3,-1)$

Radius$=3$

Hence, A is the correct option.