$\begin {array} {1 1} (A)\;1 : 2 & \quad (B)\;3 : 7 \\ (C)\;2 : 3 & \quad (D)\;2 : 5 \end {array}$

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- The distance between parallel line is $ d = \bigg| \large\frac{c_1-c_2}{\sqrt{a^2+b^2}} \bigg|$

Step 1 :

The equation of the given lines are

$ 3x+4y+5=0 $ ------(1) and

$ 3x+4y-5=0$-------(2)

Since both the lines have same slopes, the lines are parallel.

Equation of the line which divides the distances between these two lines is $3x+4y+2$--------(3)

This line also has the same slope.

Distance between lines (1) and line (3) is

$ d_1 \bigg| \large\frac{5-2}{\sqrt{3^2+4^2}} \bigg|$$ = \large\frac{3}{5}$

Distance between line (2) and line (3) is

$ d_2 = \bigg| \large\frac{-5-2}{\sqrt{3^2+4^2}} \bigg|$

$ = \large\frac{7}{5}$

Hence $d_1 : d_2 = 3 : 7$

$ \therefore $ 'B' is the correct answer.

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