Question

If the coordinates axes are the bisectors of the angles between the pair of lines ax2 + 2hxy + by2 = 0, then

Solution

Correct option is

h = 0

 

The combined equation of the angle bisectors of lines given by ax2 + 2hxy + by2 = 0, is   

                 

     

It is given that the coordinate axes are the bisectors of the angle between the lines given by ax2 + 2hxy + by2 = 0. So, their combined equation is  

                   xy = 0                                   … (ii)   

From (i) and (ii), we get h = 0, a – b ≠ 0.

SIMILAR QUESTIONS

Q1

The combined equation of the images of the pair of lines given by ax2 + 2hxy + by2 = 0 in the line mirror y = 0, is   

Q2

The difference of the tangents of the angles which the lines  make with X-axis, is 

Q3

The product of perpendiculars let fall from the point (x1y1) upon the lines represented by ax2 + 2hxy + by2, is

Q4

 

The angle between the The Pair of Straight Lines

        

Q5

The pair of lines represented by 3ax2 + 5xy + (a2 – 2)y2 = 0 are perpendicular to each other for 

Q6

 

The angle between the pair of lines represented by 2x2 – 7xy + 3y2 = 0, is   

 

Q7

The angle between the lines represented by , is

Q8

If the angle θ is acute, then the acute angle between 

Q9

If θ is the acute angle between the lines given by x2 – 2pxy + y2 = 0, then,

Q10

 bisect angles between each other, then