Highly selective Backlog Qs for JEE MainMathematicsEllipse

Two sets A and B are as under: A = a , b ∈ R × R : a - 5 < 1 and b - 5 < 1 ; B = a , b ∈ R × R : 4 a - 6 2 + 9 b - 5 2 ≤ 36 . Then :

Options

Aneither A ⊂ B nor B ⊂ A
BB ⊂ A
CA ⊂ B
DA ∩ B = ϕ (an empty set)

Correct answer

C. A ⊂ B

Step-by-step solution

Given sets, A = a , b ∈ R × R : a - 5 < 1 and b - 5 < 1 A = a , b ∈ R × R : - 1 < a - 5 < 1 and - 1 < b - 5 < 1 A = a , b ∈ R × R : 4 < a < 6 and 4 < b < 6 B = a - 6 2 9 + b - 5 2 4 ≤ 1 For set A , For corner coordinates of the set A is 4 , 4 , 4 , 6 , 6 , 4 , 6 , 3 . For set B , Now, Put 4 , 4 in the equation of the set B , 4 9 + 1 4 ≤ 1 , 4 , 4 lies in the set B . Similarly, 4 , 6 , 6 , 4 , 6 , 3 also lies in the set B . So, A ⊂ B .

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