First slide

Equation of line in Straight lines

Question

Equation of the line equidistant from the parallel lines
$9 x + 6 y - 7 = 0$ and $3 x + 2 y + 6 = 0$ is

Easy

A

6x + 4y + 5 = 0
B

18x + 12y + 11 = 0
C

18x + 12y – 11 = 0
D

12x + 8y + 7 = 0

Solution

The given lines are $3 x + 2 y + 6 = 0$ and $3 x + 2 y - \frac{7}{3} = 0$
Let the required line be $3 x + 2 y + k = 0 .$
Since it is equidistant from the given lines
$\frac{k + \frac{7}{3}}{\sqrt{9 + 4}} = \frac{6 - k}{\sqrt{9 + 4}} \Rightarrow k = \frac{11}{6}$

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