  Quantum steering ellipsoid formalism provides a faithful representation of
all two-qubit states and helps in obtaining correlation properties of the state
through the steering ellipsoid. The steering ellipsoids corresponding to the
two-qubit subsystems of permutation symmetric $N$-qubit states is analysed
here. The steering ellipsoids of two-qubit states that have undergone local
operations on both the qubits so as to bring the state to its canonical form
are the so-called canonical steering ellipsoids. We construct and analyze the
geometric features of the canonical steering ellipsoids corresponding to pure
permutation symmetric $N$-qubit states with two distinct spinors. Depending on
the degeneracy of the two spinors in the pure symmetric $N$-qubit state, there
arise several families which cannot be converted into one another through
Stochastic Local Operations and Classical Communications (SLOCC). The canonical
steering ellipsoids of the two-qubit states drawn from the pure symmetric
$N$-qubit states with two distinct spinors allow for a geometric visualization
of the SLOCC-inequivalent class of states. We show that the states belonging to
the W-class correspond to oblate spheroid centered at $(0,0,1/(N-1))$ with
fixed semiaxes lengths $1/\sqrt{N-1}$ and $1/(N-1)$. The states belonging to
all other SLOCC inequivalent families correspond to ellipsoids centered at the
origin of the Bloch sphere. We also explore volume monogamy relations of states
belonging to these families, mainly the W-class of states.
