NCERT Solutions
Class 11 Maths
Straight Lines

Ex.Misc.Q.21
Find equation of the line which is equidistant from parallel lines 9x + 6y – 7 = 0 and 3x + 2y + 6 = 0.
Given equation are:
9x + 6y - 7 = 0 ......... (1)
3x + 2y + 6 = 0 ......... (2)
Now equation of line which is equidistant from both the lines is
| (9x + 6y - 7) ÷ √ (92 + 62) | = | (3x + 2y + 6) ÷ √ (32 + 22) |
=> | (9x + 6y - 7) ÷ √ (81+36) | = | (3x + 2y + 6) ÷ √ (9 + 4) |
=> | (9x + 6y - 7) ÷ √117| = | (3x + 2y + 6) ÷ √13|
=> | (9x + 6y - 7) ÷ √117| = | (3x + 2y + 6) ÷ √13|
=> | (9x + 6y - 7) ÷ √ (13 × 9) | = | (3x + 2y + 6) ÷ √13|
=> | (9x + 6y - 7) ÷ (3 × √13) | = | (3x + 2y + 6) ÷ √13|
=> | (9x + 6y - 7) ÷ 3| = |3x + 2y + 6|
=> (9x + 6y - 7) ÷ 3 = 3x + 2y + 6 and (9x + 6y - 7) ÷ 3 = -(3x + 2y + 6)
=> 9x + 6y - 7 = 3 × (3x + 2y + 6) and 9x + 6y - 7 = -3 × (3x + 2y + 6)
=> 9x + 6y - 7 = 9x + 6y + 18 and 9x + 6y - 7 = -9x - 6y - 18
Now, 9x + 6y - 7 = 9x + 6y + 18 which is not possible.
Again
9x + 6y - 7 = -9x - 6y - 18
=> 9x + 6y - 7 + 9x + 6y + 18 = 0
=> 18x + 12y + 11 = 0
Hence, the required equation is: 18x + 12y + 11 = 0