Q. Equation of the straight line cutting off an intercept 2 from the negative direction of the axis of $y$ and inclined at $30{^\circ}$ to the positive direction of $x$-axis, is
A) $y + x - \sqrt{3} = 0$
B) $y - x + 2 = 0$
C) $y - \sqrt{3}x - 2 = 0$
D) $\sqrt{3}y - x + 2\sqrt{3} = 0$
Explanation
(d)
Let the equation of line is
$y = mx + c$
$\because m = \tan{30{^\circ}} = \frac{1}{\sqrt{3}}\ and\ c = - 2$
($\because$ It is intercepted in negative axis of $y$ with an angle $30{^\circ}$)
$\therefore$ The equation of required line is
$y = \frac{x}{\sqrt{3}} - 2$
$\Rightarrow \ \sqrt{3}y - x + 2\sqrt{3} = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.