Question

Find the equation of the line mid way between the parallel lines 9x+6y-7=0 and 3x+2y+6=0

Answer 1

Ans.

The given lines are
9x + 6y - 7 = 0
i.e., 3x + 2y - 7/3 = 0 .....(i)
and 3x + 2y + 6 = 0 .....(ii)

Let, the parallel line is
3x + 2y + k = 0 .....(iii)

Since (iii) no line passes midway between (i) and (ii), the distance between (iii) and (i); (iii) and (ii) are equal.

Thus,
|(k + 7/3)|/root over (13) = |(k - 6)|/root over (13)
or, (k + 7/3)^2 = (k - 6)^2
or, 14k/3 + 49/9 = -12k + 36
or, 50k/3 = 275/9
or, k = 11/6

Therefore, the required parallel line is
3x + 2y + 11/6 = 0
i.e., 18x + 12y + 11 = 0.