Question

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

Solution

Correct option is

 

Let  be the lines represented by the given equation. Then,

    

   

     

and,  

          

Let  be perpendicular lines. Then,  

       

   

Thus, the third line is y = m3x i.e. y = x.

SIMILAR QUESTIONS

Q1

The three lines whose combined equation is y3 – 4x2y = 0 form a triangle which is

Q2

 

The angle between the pair of lines whose equation is

 

Q3

 

If two of the straight lines represented by   are at right angles, then,

Q4

The orthocentre of the triangle formed by the pair of lines  and the line x + y + 1 = 0 is 

Q5

If the distance of a point (x1y1) from each of the two straight lines, which pass through the origin of coordinates, is δ, then the two lines are given by  

Q6

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

Q7

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

Q8

The triangle formed by the lines whose combined equation is  

Q9

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

Q10

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