Find the equation of the straight line through the point (α, β) and perpendicular to the line lx + my + n = 0.

Question

Find the equation of the straight line through the point ( α , β ) and perpendicular to the line lx + my + n = 0.

Philoid · Accepted Answer

Given: equation is perpendicular to lx + my + n = 0 and passing through (α, β)

To find:

The equation of the straight line through the point (α, β) and perpendicular to the line lx + my + n = 0.

Explanation:

The line perpendicular to lx + my + n = 0 is

mx – ly + λ = 0

This line passes through (α, β).

∴ mα-lβ + λ = 0 ⇒ λ = lβ-mα

Substituting the value of λ:

mx – ly + lβ-mα = 0

⇒ mx – α = ly – β

Hence, equation of the required line is mx – α = ly – β