The number of points with integral coordinates that are interior to the circle `x^(2)+y^(2)=16`, is

Options

A. 43
B. 49
C. 45
D. 51

Answer

C

Explanation

The circle cuts the cordinates axes at (-4, 0), (4,0), (0, 4) and (0, -4). So, the number of point is equal to the number of integral solutions , (x, y) such that `x^(2) + y^(2) lt 16`, where `-4 lt x lt 4` and `-4 lt y lt 4`

i.e., `x in [-3, 3]` and `y in [-3, 3]`
Clearly, x and y each can take 7 integral values, namely, -3, -2, -1, 0, 1, 2, 3. So, the number of ordered pairs (x, y) is 7 xx 7 = 49`.
But, out of these 49 ordered pairs (3, 3), (-3, 3), (-3, -3) and (3, -3) do not satisfy `x^(2) + y^(2) lt 16`.
Hence, required number of ordered pairs = 45.