Question

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

A

1 : 2

B

3 : 7

C

2 : 3

D

2 : 5

Solution

The correct option is C 3 : 7 Here, in all equations the coefficient of x is same. It means all the lines have same slope. So, all the lines are parallel. Now, the distance between the line 3x+4y+2=0 and 3x+4y+5=0 is given by |2−5|√32+42 =3√25=35 Again, the distance between the line 3x+4y+2=0 and 3x+4y−5=0 is given by |2+5|√32+42 =7√25=75 Hence, the ratio is given by 35:75 =3:7 Hence, the correct answer is option (b). MathematicsRD SharmaStandard XI

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