Question

$4x^{2} + y^{2} < 52,\ x,y \in Z$

↓ ↓

$${0\ \ \ \ \ \ \ \ \ 0, \pm 1, \pm 2, \pm 3, \pm 4, \pm 5, \pm 6, \pm 7\ \rightarrow \ 1 \times 15 = 15 }{\pm 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0, \pm 1, \pm 2, \pm 3\ldots\ldots\ldots. \pm 6\ \rightarrow \ 2 \times 13 = 26 }{\pm 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0, \pm 1, \pm 2, \pm 3\ldots\ldots\ldots. \pm 5\ \rightarrow \ 2 \times 11 = 22 }{\pm 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0, \pm 1, \pm 2 \pm 3\ \rightarrow \ 2 \times 7 = 14 }$$Number of elements $= 77$