The numbers of points (x,y) having integral coordinates satisfying ${\text{x}}^{\text{2}}{\text{+y}}^{\text{2}}\text{<25}$ is n then integral part of $\frac{\text{n}}{\text{9}}$ is

Since (x,y) are integers and ${\text{x}}^{\text{2}}{\text{+y}}^{\text{2}}\text{<25}$

$x,y\in \left(0,\pm 1,\pm 2,\pm 3,\pm 4\right)$

Possible number of points (x,y)=$9\times 8=81$

But the points $\left(\pm 3,\pm 4\right),\left(\pm 4,\pm 3\right),\left(\pm 4,\pm 4\right)$ lie out side the given circle

Therefore the possible number of points=

$\left(0,\pm 1,\pm 2,\pm 3,\pm 4\right)-\left(\pm 3,\pm 4\right),\left(\pm 4,\pm 3\right),\left(\pm 4,\pm 4\right)$

$=81-12=69$