Question

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

Answer 1

Answer:

10

Step-by-step explanation:

Answer 2

Total points interior of circle would be 32

1) The equation of circle can be written as x^2 + y^2 = 4^2

2) Hence the center of circle is 0,0 and radius is 4.

3) The possible points on the interior of circle would be:

First quadrant : 1,1     2,1     3,1     1,2     2,2     3,2      1,3      2,3

Second quadrant : -1,1     -2,1     -3,1     -1,2     -2,2     -3,2      -1,3      -2,3

Third quadrant :  -1,-1     -2,-1     -3,-1     -1,-2     -2,-2     -3,-2      -1,-3      -2,-3

Fourth quadrant :  1,-1     2,-1     3,-1     1,-2     2,-2     3,-2      1,-3      2,-3

4) The total number of points would be : 8*4 = 32 points

5)  Number of points on circle would be :  4 i.e.

0,4      0,-4         4,0          -4,0