First slide

Equation of line in Straight lines

Question

The equation of the line whose perpendicular distance from the origin is 3 units and the angle which the normal makes with the positive direction of x-axis is 30° is

Easy

A

$x + \sqrt{3} y = 3$
B

$\sqrt{3} x + y = 6$
C

$\sqrt{3} x + y = 1$
D

$x + \sqrt{3} y = 6$

Solution

Equation of the line is $x \cos a + y \sin a = p$ where
$p = 3, α = 30^{\circ}$ So the required equation is
$(\frac{\sqrt{3}}{2}) x + (\frac{1}{2}) y = 3$ or $\sqrt{3} x + y = 6$

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