Question

 

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

Solution

Correct option is

 

The equation  is a homogenous equation of second degree. So, it represents three straight lines passing through the origin. 

Let one of the lines be y = mx. Then, 

      

This is a cubic equation in m. So, it gives three values of m. Let the values be m1m2m3. Then,    

       

         

       

It is given that two of the three lines are at right angle. 

  

   

Since mis a root of equation (i). Therefore, 

      

SIMILAR QUESTIONS

Q1

If the equation  represents two lines inclined at an angle π, then λ =

Q2

If the equation  represents two parallel straight lines, then

Q3

The gradient of one of the lines given by  is twice that of the other, then

Q4

The equation x3 + y3 = 0 represents

Q5

 

One bisector of the angle between the lines given by

 . The equation of the other bisector is

Q6

The equation  represents two mutually perpendicular lines if

Q7

The product of the perpendiculars drawn from the point (1, 2) to be the pair of lines x2 + 4xy + y2 = 0 is

Q8

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

Q9

 

The angle between the pair of lines whose equation is

 

Q10

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