Question

Let O be the origin, A (1, 0) and B (0, 1) and P (xy) are points such thatxy > 0 and x + y < 1, then

Solution

Correct option is

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

Since xy > 0, P either lies in the first quadrant or in the third quadrant. The inequality x + y < 1 represents all points below the line x + y = 1. So that xy > 0 and x + y < 1 imply that either P lies inside the triangle OAB or in the third quadrant. 

SIMILAR QUESTIONS

Q1

The orthocenter of the triangle formed by the lines xy = 0 and x + y = 1 is 

Q2

The straight lines x + y = 0, 3x + y – 4 = 0, x + 3y – 4 = 0 form a triangle which is

Q3

If sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is

Q4

If the circumcentre of a triangle lies at the origin and centroid is the middle point of the line joining the points (a2 + 1, a2 + 1) and (2a, –2a), then the orthocenter lies on the line.

Q5

If abc are unequal and different from 1 such that the points  are collinear, then  

Q6

If two vertices of a triangle are (–2, 3) and (5, –1), orthocentre lies at the origin and centroid on the line x + y = 7, then the third vertex lies at

Q7

The line L has intercepts a and b on the coordinate axes. The coordinate axes are rotated through a fixed angle, keeping the origin fixed. If p andq are the intercepts of the line L on the new axes, then 

                                                          

Q8

If P is a point (xy) on the line, y = –3x such that P and the point (3, 4) are on the opposite sides of the line 3x – 4y = 8, then   

 

Q9

The area enclosed by 2|x| + 3|y≤ 6 is

Q10

If a line joining two points A (2, 0) and B (3, 1) is rotated about A in anticlockwise direction through and angle 15o, then equation of the line is the new position is