Two fixed charges `-2 Q ` and `Q` are located at the points with coordinates ( -3 a, 0) and (+3 a, 0) respectively in the ` X- Y` plane .
All the points in the ` X-Y` plane where the electric potential due to the two charges is zero , line on a .

Explanation

`V_(P) = (1)/(4 pi in_(0)) [(-2Q)/([(3a + x)^(2) + y^(2)]^((1)/(2)))+ (Q)/((3a - x)^(2) + y^(2))^((1)/(2))]`
`V_(p) = 0`
`(4)/((3a + x)^(2) + y^(2)) = (1)/((3a - x)^(2) + y^(2))`
`4(3a - x)^(2) + 4y^(2) = (3a + x)^(2) + y^(2)`
`4(9a^(2) - 6 ax + x^(2)) + 4y^(2) = 9a^(2) + 6 ax + x^(2) + y^(2)`
`3x^(2) + 3y^(2) - 30 ax + 27 a^(2) = 0`
`x^(2) + y^(2) - 10 ax + 9 a^(2) = 0`
This is equation of circle , hence the locus is a circle.
Center of circle `-= (5a , 0)`
Radius of circle `= sqrt((5a)^(2) - 9a^(2)) = 4a`