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