JEE Main | 2018Set, Relation and FunctionHard

Question

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

A.

A ⊂B

B.

A ∩B=ϕ(an empty set)

C.

neither A ⊂ B nor B ⊂ A

D.

B ⊂A

Solution


A = {(a, b) ∈ R×R : |a - 5| < 1, |b - 5| < 1}
Let a - 5 = x, b - 5 = y
Set A contains all points inside |x| < 1, |y| < 1
B = {(a, b) ∈ R×R : 4(a - 6)2 + 9(b - 5)2 ≤ 36}
Set B contains all points inside or on
(x-1)29+y4=1
(± 1, ±1) lies inside the ellipse ⇒ A ⊂B

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