Question

The number of points $(x,y)$ having integral co-ordinates satisfying the condition $x^2+y^2<25$ is

• A. $81$
• B. $12$
• C. $66$
• D. $69$

Answer 1

The correct option is D $69$

Since $x^2+y^2<25$ and $a$ and $y$ are integers, the
possible values of $x$ and $y\in (0,\pm 1,\pm 2,\pm 3,\pm 4,)$.
Thus,$x$ and $y$ can be chosen in $9$ ways each and $(x,y)$ can be chosen in $9\times 9=81$ ways.
However, we have to exclude cases $(\pm 3,\pm 4),(\pm 4,\pm 3)$
and $(\pm 4,\pm 4)i.e.,3\times 4=12$
Hence, the number of permissible values$=81-12=69.$