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)

$45$

Integral coordinates interior to the given circle in first quadrant are,
$(1,1),(1,2)(1,3),(2,1),(2,2),(2,3),(3,1)$
Integral coordinates on positive x-axis are $(1,0),(2,0),(3,0),(4,0)$
Also origin $(0,0)$ lie inside the given circle.
Hence total number of required points are $7\times 4+4\times 4+1=45$