Find the equation of the straight line through the point (α, β) and

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

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

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