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Let O be the origin. If A(1,0)a n dB(0,1...

Let `O` be the origin. If `A(1,0)a n dB(0,1)a n dP(x , y)` are points such that `x y >0a n dx+y<1,` then `P` lies either inside the triangle `O A B` or in the third quadrant. `P` cannot lie inside the triangle `O A B` `P` lies inside the triangle `O A B` `P` lies in the first quadrant only

A

P lies either inside the triangle OAB or in the third quadrant

B

P cannot lie inside the triangle OAB

C

P lies inside the triangle OAB

D

P lies in the first quadrant only

Text Solution

Verified by Experts

The correct Answer is:
A
Since `xy gt 0,` P lies either in the first quadrant or in the third quadrant. The inequality `x+y lt 1` represents all the points below the line x+y=1 so that `xy gt 0` and `x+y lt 1 imply that P lies either inside the triangle OAB or in the third quadrant.
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