The Combined Equation Of The Images Of The Pair Of Lines Given By ax2 + 2hxy + by2 = 0 In The Line Mirror y = 0, Is   

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Question

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

Solution

Correct option is

 

Let y = m1xy = m2x be the lines represented by

ax2 + 2hxy + by2 = 0. Then,  

          

Clearly, if y = m1x makes an angle θ1 with y = 0 (x-axis), then its image in line mirror y = 0 makes an angle –θ1 with x-axis.

So, its equation is  

      

Similarly, equation of the image of y = m2x in y = 0 is 

      y = –m2x

Therefore, the combined equation of the images is  

        

  

.         

 

Testing

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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   

Q4

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

Q5

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

Q6

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

Q7

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

Q8

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 =

Q9

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

Q10

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