Question

If z =$(\lambda +3)+i\sqrt{5-{\lambda }^2}$, then the locus of z is a

• A. circle
• B. straight line
• C. parabola
• D. none of these

Answer 1

The correct option is A circle

$z=(\lambda +3)+i\sqrt{5-{\lambda }^2}$
$\Rightarrow x=\lambda +3$ and $y=\sqrt{5-{\lambda }^2}$
eliminating $\lambda$ gives
$(x-3{)}^2+y^2=5$
$\therefore$ given locus of $z$ is a circle.
Hence, option A.