Question

Find the equation of the straight line intersecting y-axis at a distance of 2 units above the origin and making an angle of ${30}^{\circ }$ with the positive direction of the x-axis.

Answer 1

$\text{Let m be the slope of the required line.}\therefore m=tan\theta =tan{30}^{\circ }=\frac{1}{\sqrt{3}}\text{Here, c = y - intercept = 2}\text{Substituting the values of m and c in y = mx + c, we get:}y=\frac{1}{\sqrt{3}}x+2\Rightarrow x-\sqrt{3}y+2\sqrt{3}=0\text{Hence, the equation of the required line}isx-\sqrt{3}y+2\sqrt{3}=0$