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Q.
Number of points $(x, y)$ having integral coordinates satisfying the condition $x^2+y^2< 25$ is -
Conic Sections
Solution:
$x^2+y^2< 25$
Number of integral coordinate satisfying above inequality in first quadrant is $13$
i.e. $(1,1),(1,2)$, $(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),(3,1), (3,2),(3,3),(4,1),(4,2)$,
$\therefore$ Total number of integral coordinates are
$13\,\,\, 4+\underbrace{4 \times 4}_{\text {on coordinateaxes }}+\underbrace{1}_{\text {origin }}=69$
