Question

 

If one of the lines represented by the equation   is a bisector of the angle between the linesxy = 0, then λ =

Solution

Correct option is

 

We have,  

        

Thus, xy = 0 represent the coordinates axes.  

The equation of the angle bisectors between the coordinate axes are y = xand y = –x.   

It is given that one of the lines represented by the equation   

         

is     y = x or, y = –x  

  

  

.

SIMILAR QUESTIONS

Q1

The equation of the straight lines through the point (x1y1) and parallel to the lines given by 

Q2

The triangle formed by the lines whose combined equation is  

Q3

The combined equation of the pair of lines through the point (1, 0) and perpendicular to the lines represented by 

Q4

The equation x3 + ax2y + bxy2 + y3 = 0 represents three straight lines, two of which are perpendicular, then the equation of the third line is  

Q5

The combined equation of the lines L1 and L2 is 2x2 + 6xy + y2 = 0 and that of the lines L3 and L4 is 4x2 + 18xy + y= 0. If the angle between L1and L4 be α, then the angle between L2 and L3 will be   

Q6

The lines represented by  and the lines represented by  are equally inclined then

Q7

The equation  represents three straight lines passing through the origin such that

Q8

If the equation  represents two pairs of perpendicular lines, then

Q9

The equation  represents three straight lines passing through the origin such that

Q10

If θ is the angle between the straight lines given by the equation , then cosec2 θ =