Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

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

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

#### 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.

Concept: Straight Lines - Equation of Family of Lines Passing Through the Point of Intersection of Two Lines
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 23 The straight lines
Exercise 23.12 | Q 7 | Page 92
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