If z is a complex number which simultaneously satisfies the equations 3|z-12|=5|z-8 i| and |z-4|= z-8 then the Im (z) can be

Step-by-step solution

Let z=x+i y from 2^ nd equation x=6 put in (1) aligned & 3|(x-12)+y i|=5|x+(y-8) i| & 9 [36+y^2 ]=25 [36+(y-8)^2 ] (substituting x=6) & 9 36+9 y^2=25 36+25 [y^2+64-16 y ] & 16 y^2-25 16 y+36 16+25 64=0 & y^2-25 y+36+100=0 & y^2-25 y+136=0 & (y-17)(y-8)=0 aligned then, y=17 or y=8