First slide

Equation of line in Straight lines

Question

The angle which the normal to the line x – 3 y + 8 = 0 passing through the origin, makes with the positive x-axis is

Easy

A

30°
B

60°
C

120°
D

150

Solution

We write the equation of the given line in the normal
form as $- \frac{1}{2} x + \frac{\sqrt{3}}{2} y = \frac{8}{2}$
or $x \cos α + y \sin α = p,$ where $\cos α = \frac{- 1}{2},$
$\sin α = \frac{\sqrt{3}}{2}$ and $p = 4, α$ being the required angle
$\Rightarrow α = 120^{\circ}$

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