Question

find the equation of line which is equidistance from parallel line 9x + 6y -7=0 and 3x + 2y +6 = 0

Answer 1

The given parallel lines are:
9x+6y-7=0 ----(1)
3x+2y+6=0 i.e 9x+6y+18=0 -----(2) [Multiplying
b.s. by 3]
Let 9x+6y+k=0 ---(3) be the line parallel to &equidistant from the lines (1)&(2).

Then, the distance between (1)&(3) = the distance between (2)&(3)
i.e. mod (k+7) = mod (k-18)
i.e. k+7 = k-18 or k+7 = -(k-18)
i.e. 7 = - 18 or 2k = 11
i.e. k = 11/2 [ 7 = - 18 is meaningless]
Putting the value of K in (3),
9x+6y+11/2 = 0 i.e. 18x+12y+11 = 0 is the required line.

Answer 2

Answer:

The given parallel lines are:

9x+6y-7=0 ----(1)

3x+2y+6=0

[multiply by 3]

9x+6y+18=0 -----(2)

Let 9x+6y+k=0 ---(3) be the line parallel  & equidistant from the line (1) and(2).

the distance between (1)and(3) = the distance between (2)and(3)

k+7 = k-18

or, k+7 = -(k-18)

or,  7 = - 18 or 2k = 11

or, k = 11/2 ----------(4)

what we need is only k value .  

Putting (4) in (3),

9x+6y+11/2 = 0

or, 18x+12y+11 = 0 is the required line.