Elements A and B combine to form the ionic compound A_xB_y . The...

Let the number of anions B in the hcp array be $N$.

The number of octahedral voids in a close-packed structure is equal to the number of packing atoms, which is $N$.

Since cations A occupy all the octahedral voids, the number of cations A is also $N$.

The ratio of the number of atoms of A to B is $N : N = 1 : 1$.

Therefore, the formula of the compound is $\text{AB}$, which gives $x = 1$ and $y = 1$.

Answer: $x = 1$ and $y = 1$