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  • 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

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

Answers (1)

Given lines are 3x+4y+5=0…....(i) 

 3x+4y-5=0…....(ii) 

 and 3x+4y+2=0….......(iii) 

Since the coefficient of x and y are same equation i, ii and iii are parallel to each other 

 We know that in case of i and iii

distance between two parallel lines is  d=\frac{\left | c_{1}-c_{2} \right |}{\sqrt{A^{2}+B^{2}}}=\frac{\left | 5-2 \right |}{\sqrt{3^{2}+(4)^{2}}}=\frac{\left | 3 \right |}{\sqrt{9+16}}=\left | \frac{3}{5} \right |

   Similarly in case of ii and iii distance between two parallel lines is   d=\frac{\left | c_{1}-c_{2} \right |}{\sqrt{A^{2}+B^{2}}}=\frac{\left | -5-2 \right |}{\sqrt{3^{2}+(4)^{2}}}=\frac{\left | -7 \right |}{\sqrt{9+16}}=\left |- \frac{7}{5} \right | 

   Ratio between the distance is  \frac{3}{5}:\frac{7}{5}=3:7

Hence, the correct option is b

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