The equation of the locus of z such that $\bigg|\large\frac{z-i}{z+i} \bigg|$$=2$ Where $z=x+iy$ is a complex number, is

Question

\[\begin {array} {1 1} (a)\;3x^2+3y^2+10y-3=0 & \quad (b)\;3x^2+3y^2+10y+3=0 \\ (c)\;3x^2-3y^2-10y-3=0 & \quad (d)\;x^2+y^2-5y+3=0 \end {array}\]