Question

The distance between the lines y = mx + c₁ and y = mx + c₂ is ______.

विकल्प

• ${\displaystyle \frac{c_1-c_2}{\sqrt{m^2+1}}}$

• ${\displaystyle \frac{|c_1-c_2|}{\sqrt{1+m^2}}}$

• ${\displaystyle \frac{c_2-c_1}{\sqrt{1+m^2}}}$

• 0

Answer 1

The distance between the lines y = mx + c₁ and y = mx + c₂ is ${\displaystyle \frac{|c_1-c_2|}{\sqrt{1+m^2}}}$.

Explanation:

Given equations are y = mx + c₁   .....(i)

And y = mx + c₂   .....(ii)

Slopes of equation (i) and equation (ii) are same

i.e., m

So, they are parallel lines.

∴ Distance between the two lines = ${\displaystyle \frac{|c_1-c_2|}{\sqrt{1+m^2}}}$.