Question

Find the equation of the strainght line intersecting y-axis at a distance of 2 units above the origin and making an angle of 30° with the positive direction of the x-axis.

Answer 1

Let m be the slope of the required line.

$$\begin{gathered} \therefore m=\tan \theta =\tan {30}^{\circ }=\frac{1}{\sqrt{3}} \\ \mathrm{Here},c=y-\mathrm{intercept}=2 \end{gathered}$$

Substituting the values of m and c in y = mx + c, we get:

$$\begin{gathered} y=\frac{1}{\sqrt{3}}x+2 \\ \Rightarrow x-\sqrt{3}y+2\sqrt{3}=0 \end{gathered}$$

Hence, the equation of the required line is$x-\sqrt{3}y+2\sqrt{3}=0$.