Question

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 

A. 1 : 2 

B. 3 : 7 

C. 2 : 3 

D. 2 : 5

Answer 1

The distance between two parallel line 3x + 4y + 5 = 0 and 3x + 4y + 2 = 0 is 

\(\frac{|5-2|}{\sqrt{3^2+4^2}}\) = \(\frac{3}{\sqrt{25}}\) = \(\frac{3}{5}\)

The distance between two parallel line 3x + 4y + 2 = 0 and 3x + 4y - 5 = 0 is 

\(\frac{|2-(-5)|}{\sqrt{3^2+4^2}}\) = \(\frac{7}{\sqrt{25}}\) = \(\frac{7}{5}\)

Thus required ratio is = \(\frac{3}{\frac{5}{\frac{7}{5}}}\) = \(\frac{3}{7}\)