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Question

Let A and B be two sets defined as given below:
A={(x,y):|x3|<1 and |y3|<1}
B={(x,y):4x2+9y232x54y+1090}
Then,

A
AB
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B
BA
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C
A=B
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D
None of these
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Solution

The correct option is B AB
We have,
|x3|<1 and |y3|<1
2<x<4 and 2<y<4
Thus, A is the set of all points (x,y) lying inside the square formed by the lines x=2, x=4, y=2 and y=4.
Now,
4x2+9y232x54y+1090
4(x28x)+9(y26y)+1090
4(x4)2+9(y3)236
(x4)232+(y3)2221.
Thus, B is the set of all points lying inside the ellipse having its centre at (4,3) and of lengths major and minor axes are 3 and 2 units.
It can be easily seen by drawing the graphs of two regions that AB.

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