The locus of the points (in the xy-plane...

The locus of the points (in the `xy`-plane) where the electric field due to a dipole (dipole axis is along `x`-axis and its equatorial is along `y`-axis) is perpendicular to its axis, is

straight line perpendicular to the axis

circle

parabola

straight line having inclination `theta = tan^(-1)sqrt(2)` with the axis

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