Question

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

Solution

Correct option is

Two values of a

 

The pair of lines represented by the given equation will be perpendicular to each other, if  

      Coefficient of x2 + Coefficient of y2 = 0     

  

Thus, there are two values of a for which the lines represented by the given equation are perpendicular.

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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 =

Q5

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

Q6

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

Q7

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

Q8

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

Q9

 

The angle between the The Pair of Straight Lines

        

Q10

 

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