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  • A point P (x, y) is said to be integral point iff both x, y are integers. Then number of integer points inside or on the circle <img alt="\mathrm{x^2+y^2=9}" src="https://entrancecorner.oncodecogs.

A point P (x, y) is said to be integral point iff both x, y are integers. Then number of integer points inside or on the circle \mathrm{x^2+y^2=9} is

Option: 1

10


Option: 2

81


Option: 3

39

 


Option: 4

29


Answers (1)

best_answer

Let (n, m) be a integer point, then

\mathrm{n^2+m^2 \leq 9}

\mathrm{\text { if } \mathrm{n}^2=9, \mathrm{~m}^2=0 \Rightarrow 2 \times 1=2 \text { points }}

\mathrm{\text { if } n^2=4, m^2=0,1,4 \Rightarrow 2 \times 5=10 \text { points }}

\mathrm{\text { if } n^2=1, m^2=0,1,4 \Rightarrow 2 \times 5=10 \text { points }}

\mathrm{\text { if } \mathrm{n}^2=0, \mathrm{~m}^2=0,1,4,9 \Rightarrow 1 \times 7=7 \text { points }}

so in total, we have 29 points, which are integral points.

 

Posted by

HARSH KANKARIA

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