Question #d9d7d

1 Answer
Jan 25, 2018

Place of #(x, y)# was a circle with its center was #M (0, 0)# and its radius was #r=3#.

Explanation:

Set #z=x+yi#. Hence,

#|z+9|=3*|z+1|#

#|x+yi+9|=3*|x+yi+1|#

#|(x+9)+yi|=3*|(x+1)+yi|#

#sqrt((x+9)^2+y^2)=3*sqrt((x+1)^2+y^2)#

#(x+9)^2+y^2=9*((x+1)^2+y^2)#

#x^2+18x+81+y^2=9x^2+18x+9+9y^2#

#8x^2+8y^2=72#

#x^2+y^2=9#

I found a circle with its center was #M (0, 0)# and its radius was #r=3#.