Let R denote the set of all real numbers. Let z_1=1+2 i and z_2=3 i be two complex numbers, where i= -1 . Let S= \ (x, y) R R : |x+i y-z_1 |=2 |x+i y-z_2 | \ . Then which of the following statements is (are) TRUE?

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Correct answer: D. S is a circle with radius 2 2 3

aligned & aligned & |x+i y-1-2 i|=2|x+i y-3 i| \ & (x-1)^2+(y-2)^2=4 (x^2+(y-3)^2 ) \ & 3 x^2+3 y^2+2 x-20 y+31=0 \ & x^2+y^2+ 2 x 3 - 20 y 3 + 31 3 =0 aligned \ & S is a circle with centre (- 1 3 , 10 3 ) and radius = 1 9 + 100 9 - 31 3 = 8 9 = 2 2 3 aligned

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