QJEEM22Mabdce: JEE Main 2022 Mathematics - Class 11 JEEM22Mabdce Solution:  Let  S = { ( x , y ) ∈ N × N : 9 ( x − 3 ) 2 + 16 (…

$S=\left\{(x, y) \in \mathbb{N} \times \mathbb{N}: \frac{(x-3)^{2}}{16}+\frac{(y-4)^{2}}{9} \leq 1\right\}$

represents all the integral points inside

and on the ellipse $\frac{(x-3)^{2}}{16}+\frac{(y-4)^{2}}{9}=1$ , in first quadrant.

and $T=\left\{(x, y) \in \mathbb{R} \times \mathbb{R}:(x-7)^{2}+(y-4)^{2} \leq 36\right\}$ represents all the points on

and inside the circle $(x-7)^{2}+(y-4)^{2}=36$


$\therefore \quad n(S \cap T)=\{(3,1),(2,2),(3,2),(4,2),(5,2)$ , $(2,3), \ldots(6,5)\}$

Total number of points $=27$