Question

If one of the lines given by ax2 + 2hxy + by2 = 0 may be perpendicular to one of the lines given by ax2 + 2hxy + by2 = 0, then (aa’ – bb’)2 =

Solution

Correct option is

 

We have, 

       

and, 

       

Let y = mx be one of the lines represented by (i). Then y = mx satisfy (i),  

  

  

The equation of a line passing through the origin and perpendicular to y =mx, is    

       

Since one of the lines given by (i) is perpendicular to one of the lines given by ax2 + 2hxy + by2 = 0. Therefore, one of the lines given by (ii) is myx = 0   

Hence, my + x = 0 i.e., x = –my satisfy equation (ii)   

Using cross-multiplication in (iii) and (iv), we have 

      

This is the required condition.

SIMILAR QUESTIONS

Q1

If the sum of the slopes of the lines given by 4x2 + 2kxy – 7y2 = 0 is equal to the product of the slopes, then k =

Q2

If the sum of the slopes of the lines given by x2 + 2cxy – y2 = 0 is four times their product, then c has the value

Q3

If the slopes of the lines given by ax2 + 2hxy + by2 = 0 are in the ratio 3 : 1, then h2 =

Q4

If the slope of one line in the pair ax2 + 4xy + y2 = 0 is three times the other, then a =  

Q5

The combined equation of the pair of lines through the origin and perpendicular to the pair of lines given by ax2 + 2hxy + by2 = 0, is   

Q6

Equation of The Pair of Straight Lines drawn through (1, 1) and perpendicular to the pair of lines 3x2 – 7xy + 2y2 = 0, is

Q7

The equation to the pair of lines perpendicular to the pair of lines 3x2 – 4xyy2 = 0, is

Q8

If the slope of one of the lines given by ax2 + 2hxy + by2 = 0 is 5 times the other, then

Q9

If the pair of lines ax2 + 2hxy + by2 = 0 and ax2 + 2hxy + by2 = 0 have one line in common, then (ab’ – ab)2 =

Q10

If the slope of one of the lines represented by ax2 + 2hxy + by2 = 0 be the square of the other, then