Find the distance between parallel lines. l(x + y) + p = 0 and l(… - Vidyadip

Question

Find the distance between parallel lines. l(x + y) + p = 0 and l(x + y) - r = 0

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Answer

We have the equation,
lx + ly + p = 0
and lx + ly - r = 0
where a = 1, b = 1 , c₁ = p and c₂ = -r
$\therefore$ The distance between two parallel lines
d = $\frac{{\left| {{c_1} - {c_2}} \right|}}{{\sqrt {{a^2} + {b^2}} }}$
$\Rightarrow \frac{{\left| {p + r} \right|}}{{\sqrt {{1^2} + {1^2}} }}$
$\Rightarrow \frac{1}{{\sqrt 2 }}\left| {\frac{{p + r}}{1}} \right|$ units

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