What is the radiation pattern of a dipole antenna in free space in a plane containing the conductor?
Why A half-wave dipole radiates most strongly broadside, at right angles to the wire, and has deep nulls off the wire ends because the current elements cancel in that direction. In the plane that contains the conductor, plotting relative field strength versus angle traces two lobes perpendicular to the wire, the classic figure-eight. In the plane perpendicular to the wire, the same antenna is omnidirectional, which is why the question specifies which plane you are looking at.
Watch out The figure-eight off the ends is backwards: the ends are where a dipole radiates least. The circular pattern is what you see in the plane at right angles to the conductor, not the plane containing it.
A dipole shouts sideways and whispers off its ends: figure-eight broadside, nulls at the tips.