Question

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

(Given $\lambda$ is any real number)

• A. $|z+3|=5$
• B. $|z-3|=5$
• C. $|z-3|=\sqrt{5}$
• D. $|z+3|=\sqrt{5}$

Answer 1

Answer: (C)

$|z-3|=\sqrt{5}$

Let z=x+iy
$\therefore$ $x=\lambda +3$
$y=\sqrt{5-{\lambda }^2}$
$y^2=5-(x-3{)}^2$
$\therefore (x-3{)}^2+y^2=5$
$|z-z_0|=\sqrt{5}$
where $z_0=(3,0)$
$\therefore |z-3|=\sqrt{5}$