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

Answer: (A)

Let $z=x+iy$.
Then $x=\lambda +3$ and $y=\sqrt{5-{\lambda }^2}$
$\Rightarrow (x-3{)}^2={\lambda }^2$(1)
and $y^2=5-{\lambda }^2$(2)
From (1) and (2), $(x-3{)}^2=5-y^2$
$\Rightarrow (x-3{)}^2+y^2=5$.
Obviously it is a circle.