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