If z=(λ+3)+i(5−λ2) ; then the locus of z  is (where i=−1 )

Since z=(λ+3)+i(5−λ2) Let      z=x+iy Then x+iy=(λ+3)+i(5−λ2) Comparing the real and imaginary parts, then             x=λ+3⇒x−3=λ                       ……..(i)and      y=5−λ2 or      y=5−(x−3)2      [from Eq. (i)]which is a part of circle.