(c1-c2)/

Here

ax+by+c₁=0-->(1)               ax+by+c₂=0-->(2)

Let P(x₀,y₀) be a point on the straight line (1)

so that ax₀+by₀=-c₁-->(3)

Now the distance between the parallel lines (1),(2) is equal to

PM where PM is the perpendicular distance of P from (2)

and hence

PM= [by length of perpendicular]

from (3)

=|-c₁+c₂| / root over (a²+b²)

=|c₂-c₁| / root over (a²+b²)

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