Question

If $Z=(\lambda +3)+i\sqrt{3-{\lambda }^2}$, for all real $\lambda$ then locus of Z is

• A. Circle
• B. Parabola
• C. Line
• D. None of these

Answer 1

Answer: (A)

Circle

$Z=(\lambda +3)+i\sqrt{3-{\lambda }^2}$

For real number = 0

$\lambda +3=0$

$\lambda =-3$

$Z=0+i\sqrt{3-(9{)}^2}$

If $Z=x+iy$

$y=-\sqrt{6}x$

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

Hence locus is circle