Question

Find the ratio in which the line $3x+4y+2=0$ divides the distance between the lines $3x+4y+5=0$ and $3x+4y-5=0$.

Answer 1

Here, in all equations the coefficient of $x$ is same.

It means all the lines are parallel.

Now, the distance between the line $3x+4y+2=0$ and $3x+4y+5=0$ is given by $\frac{|2-5|}{\sqrt{3^2+4^2}}$

$=\left|\frac{3}{\sqrt{25}}\right|=\frac{3}{5}$

Again, the distance between the line $3x+4y+2=0$ and $3x+4y-5=0$ is given by $\frac{|2-5|}{\sqrt{3^2+4^2}}$

$=\left|\frac{7}{\sqrt{25}}\right|=\frac{7}{5}$

Hence, the ratio is given by

$\frac{3}{5}:\frac{7}{5}$

$=3:7$