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  • The number of points with integral coordinates that are interior to the circle is<div cl

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

Option: 1

43


Option: 2

49


Option: 3

45


Option: 4

51


Answers (1)

best_answer

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. The number of

selections of values of x is 7 , namely -3,-2,-1,0,1,2,3. The same is true for y. So the number  of ordered pairs

(x, y)$ is $7 \times 7. But (3,3),(3,-3),(-3,3),(-3,-3) are rejected because they do not satisfy the inequation

x^2+y^2<16.
So the number of points is 45 .

Posted by

vishal kumar

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