Question

Find the distance between parallel lines 9x + 6y − 7 = 0 and 3x + 2y + 6 = 0

Answer 1

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"`.