Question

If the pair of lines represented by ax2 + 2hxy + by2 = 0, b  0, are such that the sum of the slopes of the lines is three times the product of their slopes, then   

Solution

Correct option is

3+ 2h = 0

 

Let y = m1x and y = m2x be the lines  represented by

ax2 + 2hxy + by2 = 0. Then,   

      

It is given that 

      

  

.

SIMILAR QUESTIONS

Q1

If the equation 2x2 + λ xy + 2y2 = 0 represents a pair of a real and distinct lines, then    

Q2

 

The two straight lines given by 

      

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

Q3

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 =

Q4

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

Q5

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

Q6

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

Q7

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   

Q8

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

Q9

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

Q10

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