Let and . Then [2025]

Question

Let $A = {(α, β) \in R \times R : | α - 1 | \leq 4 and | β - 5 | \leq 6}$ and $B = {(α, β) \in R \times R : 16 {(α - 2)}^{2} + 9 {(β - 6)}^{2} \leq 144}$ . Then [2025]

Smart Achievers · Accepted Answer

(3)

$A : | α - 1 | \leq 4 and | β - 5 | \leq 6$

$\Rightarrow - 4 \leq α - 1 \leq 4 and - 6 \leq β - 5 \leq 6$

$\Rightarrow - 3 \leq α \leq 5 and - 1 \leq β \leq 11$

$B : 16 {(α - 2)}^{2} + 9 {(β - 6)}^{2} \leq 144$

$B : \frac{{(α - 2)}^{2}}{9} + \frac{{(β - 6)}^{2}}{16} \leq 1$

From Diagram, $B \subset A$ .

Solution

Q.
Let $A = {(α, β) \in R \times R : | α - 1 | \leq 4 and | β - 5 | \leq 6}$ and $B = {(α, β) \in R \times R : 16 {(α - 2)}^{2} + 9 {(β - 6)}^{2} \leq 144}$ . Then [2025]

1 $A \subset B$

2 neither $A \subset B$ nor $B \subset A$

3 $B \subset A$

4 $A \cup B = {(x, y) : - 4 \leq x \leq 4, - 1 \leq y \leq 11}$

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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}