Question

Find the equation of the line of shortest distance between two lines

Answer 1

Answer:

If we have two lines considering the genral equation:

$y =mx+c_1$

$y=mx+c_2$

Where, m is the slope of the line.

Then the shortest distance between two lines is:

$d=\frac{|c_2-c_1|}{\sqrt{1+m^2}}$

And if the lines are parallel that is the equation is in the form:

$ax+by+d_1=0$

And$ax+by+d_2=0$

Then, the shortest distance between the lines is:

$d=\frac{|d_2-d_1|}{\sqrt{a^2+b^2}}$