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  4. 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

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Q. Two sets $A$ and $B$ are as under:
$A = \{(a, b) \in R \times R : |a - 5| < 1$ and $|b - 5| < 1\} $;
$B = \{(a, b) \in R \times R : 4(a - 6)2 + 9(b - 5)^2 \leq 36\}$. Then

JEE MainJEE Main 2018Conic Sections

Solution:

As, $|a-5|<1$ and $|b-5|<1$
$\Rightarrow 4< a , b <6$ and $\frac{(a-6)^{2}}{9}+\frac{(b-5)^{2}}{4} \leq 1$
Taking axes as $a$-axis and $b$-axis
image
The set $A$ represents square $PQRS$ inside set $B$ representing ellipse and hence $A \subset B$.