Question

Find the distance between parallel lines 4x − 3y + 5 = 0 and 4x − 3y + 7 = 0

Answer 1

Equations of the given parallel lines are 

4x − 3y + 5 = 0 and 4x − 3y + 7 = 0

Here, a = 4, b = − 3, c₁ = 5 and c₂ = 7

∴ Distance between the parallel lines

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

= `|(5 - 7)/sqrt(4^2 + (-3)^2)|`

= `|(-2)/sqrt(16 + 9)|`

= `|(-2)/5|`

= `2/5"units"`