Question

Find the number of point $(x,y)$ having integral coordinates satisfying the condition $x^2+y^2<25$.

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

Answer 1

The correct option is D

$69$

Step:1 Calculate the total number of pairs for the values of$(x,y)$.

Here, the given equation is$x^2+y^2<25$.

The values of $x$ and $y$ can be $(0,\pm 1,\pm 2,\pm 3,\pm 4)$ as those values satisfy the above mentioned condition.

Therefore, there are $9$ different values that are possible.

Hence, a pair of values of $(x,y)$ can be selected in $9^2$ ways = $81$ ways.

However, for the certain pair values of$(x,y)$, the above equation does not satisfy. Those are$(\pm 3,\pm 4),(\pm 4,\pm 3),(\pm 4,\pm 4)$.

Therefore, a total number of $3\times 4=12$ pair of values of $(x,y)$ must be eliminated.

Step: Calculate the number of points.

Hence, the required number of points $$\begin{gathered} =81-12 \\ =69 \end{gathered}$$

Therefore, Option(B) is the correct answer.