Question

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

Solution

Correct option is

 

Let the equation of the common line be mx. Then, it must satisfy both the given equations.  

and, 

         

  

  

  

    

  

which is the required condition.

SIMILAR QUESTIONS

Q1

 

The two straight lines given by 

      

make with the axis of x angle such that the difference of their tangents is

Q2

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 =

Q3

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

Q4

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

Q5

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

Q6

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   

Q7

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

Q8

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

Q9

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

Q10

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 =