Question

The locus of the points representing complex number $z=x+iy$ for which $|z+5{|}^2-|z-5{|}^2=10$ is

• A. $x+y=2$
• B. $y=\frac{1}{2}$
• C. $x=\frac{1}{2}$
• D. $x+y=10$

Answer 1

The correct option is C $x=\frac{1}{2}$

$|z+5{|}^2-|z-5{|}^2=10\Rightarrow (x+5{)}^2+y^2-[(x-5{)}^2+y^2]=10\Rightarrow 10\times 2x=10$
Hence, the locus of $z$ is $x=\frac{1}{2}$