$\mathrm{X}$ and $\mathrm{Y}$ are anhydrides of sulphurous and sulphuric acid respectively. The hybridisation state and the shape of $\mathrm{X}$ and $\mathrm{Y}$ are

 

The anhydrides of sulphurous and sulphuric acid are ${\mathrm{SO}}_2$  and ${\mathrm{SO}}_3$ respectively.

The hybridisation and shape of ${\mathrm{SO}}_2$  and ${\mathrm{SO}}_3$ are ${\mathrm{sp}}^2$, angular and ${\mathrm{sp}}^2$, planar triangular.