Question

The number of points with integral coordinates that are interior to the circle $x ^ { 2 } + y ^ { 2 } = 16$ is

• A. 43
• B. 49
• C. 45
• D. 51

Answer 1

Answer: (C)

45

Answer 2

The number of points is equal to the number of integral solutions (x, y) such that $x ^ { 2 } + y ^ { 2 } < 16$.

So, x, y are integers such that $- 3 \leq x \leq 3 , - 3 \leq y \leq 3$ satisfying the inequation $x ^ { 2 } + y ^ { 2 } < 16$

So the number of points is 45.