The given parallel lines are
9x + 6y – 7 = 0 …(1)
3x + 2y + 6 = 0.
⇒ 9x + 6y + 18 = 0 …(2)
Let the line which is equidistant from (1) and (2) be 9x + 6y + \(\lambda\)= 0 …(3)
Distance between (1) and (2) = \(^\frac{|7 - \lambda|}{\sqrt{9^2+6^2}}\) = \(^\frac{|7+ \lambda|}{\sqrt{117}}\)
and distance between (2) and (3) = \(^\frac{|18 - \lambda|}{\sqrt{9^2+6^2}}\)=\(^\frac{|18 - \lambda|}{\sqrt{117}}\)
Given,
\(^\frac{|7+ \lambda|}{\sqrt{117}}\)=\(^\frac{|18 - \lambda|}{\sqrt{117}}\)
⇒ 7 + \(\lambda\) = 18 – \(\lambda\) ⇒ \(\lambda\) = \(\frac{11}{2}\)
The equation of the required line is
9x + 6y +\(\frac{11}{2}\) = 0
⇒ 18x + 12y + 11 = 0
