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Solution


Q.

Let A={(α,β)∈R×R:|α–1|≤4 and |β–5|≤6} and B={(α,β)∈R×R:16(α–2)2+9(β–6)2≤144}. Then          [2025]
1 A⊂B  
2 neither A⊂B nor B⊂A  
3 B⊂A  
4 A∪B={(x,y):–4≤x≤4,–1≤y≤11}  

Ans.

(3)

A:|α–1|≤4 and |β–5|≤6

⇒  –4≤α–1≤4 and –6≤β–5≤6

⇒  –3≤α≤5 and –1≤β≤11

B:16(α–2)2+9(β–6)2≤144

B:(α–2)29+(β–6)216≤1

From Diagram, B⊂A.