Question
Question: Equation of the line which is parallel to the line common to the pair of lines given by 6x<sup>2</su...
Equation of the line which is parallel to the line common to the pair of lines given by 6x2 – xy – 12y2 = 0 and
15x2 + 14xy – 8y2 = 0 and the sum of whose intercepts on the axes is 7, is
A
2x – 3y = 42
B
3x + 4y = 12
C
5x – 2y = 10
D
None of these
Answer
3x + 4y = 12
Explanation
Solution
6x2 – xy – 12y2 = 0
Ž (2x – 3y) (3x + 4y) = 0 ….(i)
and 15x2 + 14xy – 8y2 = 0
Ž (5x – 2y) (3x + 4y) = 0 ….(ii)
Equation of the line common to (i) and (ii) is
3x + 4y = 0
Equation of any line parallel to (ii) is
3x + 4y = k or 
+ 
= 1
If 
+ 
= 7, then k = 12 and the equation of the required line is 3x + 4y = 12