Question

Find the distance between the parallel lines 15x + 8 y - 34 = 0, 15 x +8y +31 = 0.

Answer 1

As we know that distance between the parallel lines $\left(d\right)$ is given as-

$d=\frac{|c_2-c_1|}{\sqrt{a^2+b^2}}$

Given lines:-

$15x+8y-34=0$

$15x+8y+31=0$

Here,

$a=15,b=8,c_1=-34,c_2=31$

Therefore,

$d=\frac{|31-(-34)|}{\sqrt{{\left(15\right)}^2+{\left(8\right)}^2}}$

$\Rightarrow d=\frac{\left|65\right|}{\sqrt{225+64}}$

$\Rightarrow d=\frac{65}{17}=3.82\text{units}$

Hence the distance between the given parallel lines is $3.82$ units.