Question

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   

Solution

Correct option is

bx2 – 2hxy + ay2 = 0

 

Let y = m1x and y = m2x be the lines respected by ax2 + 2hxy + by2 = 0. Then, 

         

The equations of the lines passing through the origin and perpendicular toy = m1x and y = m2x respectively are    

        m1y + x = 0 and m2y + x = 0 

The combined equation of these lines is  

       (m1y + x)(m2y + x) = 0   

  

  

    

Note : The equation of the pair of lines through the origin and perpendicular to the pair of lines given by ax2 + 2hxy + by2 = 0 can be obtained by interchanging the coefficients of x2 and y2 and changing the sign of the term conaining xy.

SIMILAR QUESTIONS

Q1

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

Q2

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   

Q3

 

The two straight lines given by 

      

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

Q4

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 =

Q5

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

Q6

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

Q7

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

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