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Question

Find the distance between parallel lines

(i) 15x + 8y - 34 = 0 and 15x + 8y + 31 = 0

(ii) l(x + y) + p = 0 and l(x + y) - r = 0


Solution

(i) The given equations are

15x + 8y - 34 = 0

and 15x + 8y + 31 = 0

where a = 15, b = 8, c1

= - 34 and c2 = 31

The distance between two parallel lines

d=|c1c2|a2+b2

   |3431|(15)2+(8)2 6517units

(ii) We have the equation

lx + ly + p = 0

and lx + ly - r = 0

where a = 1, b = 1, c1 = p

and c2=r

The distance between two parallel lines

    |p+r|l2+l212p+rl units

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