First slide

Equation of line in Straight lines

Question

The equation of a straight line on which the length of perpendicular from the origin is four units and the line makes an angle of $120^{0}$ with the x-axis is

Moderate

A

$x \sqrt{3} + y + 8 = 0$
B

$x \sqrt{3} - y = 8$
C

$x \sqrt{3} + y = 8$
D

$x + \sqrt{3} y + 8 = 0$

Solution

Given that the slope is $- \sqrt{3},$
Therefore, the line is

$y = - \sqrt{3} x + c$
or $\sqrt{3} x + y = c$
Now, $|\frac{c}{2}| = 4$ or $c = \pm 8$

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