Let z∈C, the set of complex numbers. Then the equation, 2|z+3i|−|z−i|=0 represents.

The correct option is B A circle with radius 83
Given: ⇒2|z+3i|−|z−i|=0.. (1)
Substituting z=x+iy in (1), ⇒2|x+i(y+3)|=|x+i(y−1)| ⇒2√x²+(y+3)²=√x²+(y−1)²
⇒4x²+4(y+3)²=x²+(y−1)²
⇒3x²=y²−6y+1−4y²−24y−36
⇒3x²+3y²+18y+35=0
⇒x²+y²+6y+35/3=0
This is the equation of the circle ∴radius=r=√0+9−35/3=√(27−35)/3=√−8/3 which is not possible.
Let's correct the solution:
2|z+3i|=|z-i|
Squaring both sides:
4|z+3i|²=|z-i|²
4(x²+(y+3)²) = x²+(y-1)²
4x²+4(y²+6y+9) = x²+y²-2y+1
4x²+4y²+24y+36 = x²+y²-2y+1
3x²+3y²+26y+35=0
3(x²+y²)+26y+35=0
Dividing by 3:
x²+y²+26/3y+35/3=0
This is the equation of a circle with center at (0, -13/3) and radius r = √((13/3)²-35/3) = √(169/9 - 105/9) = √(64/9) = 8/3
Therefore radius = 8/3