Question

Find the distance between parallel lines 9x + 6y − 7 = 0 and 9x + 6y − 32 = 0.

Answer 1

Equations of the given parallel lines are 9x + 6y − 7 = 0 and 9x + 6y − 32 = 0.
Here, a = 9, b = 6, C₁ = –7 and C₂ = –32
∴ Distance between the parallel lines

= `|("C"_1 - "C"_2)/sqrt("a"^2 + "b"^2)|`

= `|(-7 - (-32))/sqrt(9^2 + 6^2)|`

= `|(-7 + 32)/sqrt(81 + 36)|`

= `|25/sqrt(117)|`

= `25/sqrt(117)` units.