The ratio in which the line 3x + 4y + 2 = 0 divides the distance between the lines 3x + 4y + 5 = 0 and 3x + 4y – 5 = 0 is

Given lines are:

3x + 4y + 5 = 0 …(i)

3x + 4y – 5 = 0 …(ii)

and 3x + 4y + 2 = 0 …(iii)

Clearly, eq. (i), (ii) and (iii) are parallel to each other as the coefficients of x and y are same.

We know that,

distance between two parallel lines is

Distance between parallel lines

3x + 4y + 5 = 0

3x + 4y + 2 = 0

Distance between parallel lines

3x + 4y – 5 = 0

3x + 4y + 2 = 0

∴ Ratio between the distance is

Hence, the correct option is (b)