Electrostatics

(a) All points in x-y plane where the potential is zero lies on a circle.

Let q be the test charge.

At all the points of zero potential i.e. (x,y) this test charge will not experience any electrostatic force.

2Qq/((x+3a)²+y²) = Qq/((x-3a)²+y²)

2((x-3a)²+y²) = (x-3a)²+y²

As we can see by further simplification of the above expression, that the locus will have quadratic terms in x and y. Further it's a circle.

Regards,

Team,

TopperLearning.