Mathematics (2018) | JEE 2018 | Discussion Page

Two sets A and B are as under A= { (a,b)} $\in$ RxR: $\mid a-5\mid<1$ and $\mid b-5\mid<1$ ; B={(a,b) $\in$ RxR:

$4(a-6)^{2}+9(b-5)^{2}\leq 36$ } , Then

$B\subset A$

$A\subset B$

$A\cap B =\phi$ (an empty set)

D) neither

$A\subset B$ nor

$B\subset A$

Option B

We have

$\mid a-5\mid<1$ and $\mid b-5\mid<1$

$\therefore$ -1 < a - 5< 1 and -1 < b-5 < 1

$\Rightarrow$ 4<a<6 and 4<b<6

Now , $4(a-6)^{2}+9(b-5)^{2}\leq 36$

$\Rightarrow$ $\frac{(a-6)^{2}}{9}+\frac{(b-5)^{2}}{4}\leq1$

Taking axes as a-axis and b-axis

The set A represents square PQRS inside set B representing ellipse and hence $A\subset B$

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