Given sets, A=(a,b)∈R×R:∣a−5∣<1and∣b−5∣<1
A=(a,b)∈R×R:−1<a−5<1and−1<b−5<1
A=(a,b)∈R×R:4<a<6and4<b<6
B=9(a−6)2+4(b−5)2≤1
For set A,

For corner coordinates of the set Ais (4,4),(4,6),(6,4),(6,3).
For set B,

Now, Put (4,4)in the equation of the set B,
94+41≤1,(4,4)lies in the set B.
Similarly, (4,6),(6,4),(6,3)also lies in the set B.
So, A⊂B.