Question

Question 6 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

Class X1 - Maths -Straight Lines Page 227

Answer 1

Distance between two parallel lines ax + by + c = 0 and ax + by + K = 0 is
|K - c |/√(a² + b²)


(i) lines are 15x + 8y - 34 = 0 and 15x + 8y +31=0
so, distance between two lines = |31 -(-34)|/√(15²+8²)
=|31 + 34|/√(225 + 64)
= 65/√289
= 65/17 units


(ii) lines are lx +ly + h = 0 and lx + ly -r = 0
so, distance between two lines= |-r - h|/√(l²+l²)
= |-(r+h)|/√2l²
=| (r + h)/√2l | units