The ratio in which the line 3x + 4y + 2 = 0 divides the distance betwe

1.	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» 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 = \(\frac{3}{\frac{5}{\frac{7}{5}}}\) = \(\frac{3}{7}\)

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»

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 = \(\frac{3}{\frac{5}{\frac{7}{5}}}\) = \(\frac{3}{7}\)