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Question
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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Solution
The line perpendicular to lx + my + n = 0 is \[mx - ly + \lambda = 0\]
This line passes through (α, β).
\[\therefore m\alpha - l\beta + \lambda = 0\]
\[ \Rightarrow \lambda = l\beta - m\alpha\]
Substituting the value of \[\lambda\]:
\[mx - ly + l\beta - m\alpha = 0\]
\[ \Rightarrow m\left( x - \alpha \right) = l\left( y - \beta \right)\]
This is equation of the required line.
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