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JEE Main202229 Jul 2022Evening ShiftMathematicsEllipseActual

Let S = x , y ∈ ℕ × ℕ : 9 x - 3 2 + 16 y - 4 2 ≤ 144 and T = x , y ∈ ℝ × ℝ : x - 7 2 + y - 4 2 ≤ 36 The n S ∩ T is equal to ______.

Correct answer

0

Step-by-step solution

Given, S :   9 ( x - 3 ) 2 + 16 y - 4 2 ≤ 144   where  x , y ∈   N × N On rearranging we get, S : ( x - 3 ) 2 16 + y - 4 2 9 ≤ 1   where  x , y ∈ 1 , 2 , 3 , … … Now T : x - 7 2 + y - 4 2 ≤ 36   where  x , y ∈ R Now let x - 3 = X : y - 4 = Y So, new equation and domain will become, S : X 2 16 + Y 2 9 ≤ 1 ;   X ∈ - 2 , - 1 , 0 , 1 , … … T : X - 4 2 + Y 2 ≤ 36 ;   Y ∈ - 3 , - 2 ,

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