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

Answer 1

It is known that the distance (d) between parallel lines Ax + By + C₁ = 0 and Ax + By + C₂ = 0 is given by.

(i) The given parallel lines are 15x + 8y – 34 = 0 and 15x + 8y + 31 = 0.

Here, A = 15, B = 8, C₁ = –34, and C₂ = 31.

Therefore, the distance between the parallel lines is

(ii) The given parallel lines are l (x + y) + p = 0 and l (x + y) – r = 0.

lx + ly + p = 0 and lx + ly – r = 0

Here, A = l, B = l, C₁ = p, and C₂ = –r.

Therefore, the distance between the parallel lines is