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Question
Find the distance between parallel lines 9x + 6y − 7 = 0 and 3x + 2y + 6 = 0
Solution
First we write the equations of the two lines in such a way that the coefficients of x and y are same in the two equations.
For this purpose, we multiply the second equation by 3.
Then the equations of the two lines are:
9x + 6y − 7 = 0 and 9x + 6y + 18 = 0
∴ the distance between parallel lines
= `|("c"_1 - "c"_2)/sqrt("a"^2 + "b"^2)|`,
where c1 = −7, c2 = 18, a = 9, b = 6
= `|(-7 - 18)/sqrt(9^2 + 6^2)|`
= `|(-25)/sqrt(81 + 36)|`
= `|25/sqrt(117)|`
= `25/(3sqrt(13))"units"`.
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