Question

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   

Solution

Correct option is

 

We observe that the combined equation of the bisectors of the angles between the lines in the first pair is  

       

and that of the second pair is  

         

Clearly, equations (i) and (ii) are same. Thus, the two pairs of lines have the same bisector. Consequently, they are equally inclined to each other. Hence, the angle between L2 and L3 is also α.

SIMILAR QUESTIONS

Q1

 

The angle between the pair of lines whose equation is

 

Q2

 

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

Q3

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

Q4

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  

Q5

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

Q6

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

Q7

The triangle formed by the lines whose combined equation is  

Q8

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

Q9

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

Q10

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