Question

The axes being inclined at an angle of ${30}^o$, the equation of straight line which makes an angle of ${60}^o$ with the positive direction of x-axis and x-intercept 2 is

• A. $y-\sqrt{3}x=0$
• B. $\sqrt{3}y=x$
• C. $y+\sqrt{3}x=2\sqrt{3}$
• D. $y+2x=0$

Answer 1

The correct option is C $y+\sqrt{3}x=2\sqrt{3}$

$m=\frac{\sin {60}^o}{\sin ({30}^o-{60}^o)}=-\sqrt{3}$
Therefore, the equation of the line is $y-0=-\sqrt{3}(x-2)$, i.e. $\sqrt{3}x+y=2\sqrt{3}$.