Locus is a circle (equation depends on choice of coordinate system)

Sol. Let charge q and –2q are placed in x – y plane and at x – axis; Co-ordinate of q and –2q are respectively (–3, 0) and (3, 0). Let a point (x, y) is in the plane at which net potential is equal to zero

∴ + = 0

⇒ 4 [(x + 3) 2 + y 2 ] = [(x – 3) 2 + y 2 ]

⇒ 4x 2 + 24x + 36 + 4y 2 = x 2 + 9 – 6x + y 2 ∴ 3x

2 + 3y 2 + 30x + 27 = 0

∴ x 2 + y 2 + 10x + 9 = 0

Or (x + 5) 2 + (y – 0) 2 = 16

This is eq n of circle of radius 4m and center at (–5, 0)