Question

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

Answer 1

Let $AB$ intersect the $y-$axis at $2$ units above origin.

At $y-$axis,$x$ will always be $0$

$\therefore$ Line $AB$ cuts $y-$axis at $P(0,2)$

Also, line $AB$ makes an angle of ${30}^{\circ }$ with the $x-$axis.

$\therefore$ Slope$=\tan \theta =\tan {30}^{\circ }=\frac{1}{\sqrt{3}}$

We know that equation of line passing through $(x_0,y_0)$ and having slope $m$ is

$y-y_0=m(x-x_0)$

Here $x_0=0,y_0=2$ and $m=\frac{1}{\sqrt{3}}$

Putting these values in $y-y_0=m(x-x_0)$

$y-2=\frac{1}{\sqrt{3}}(x-0)$

$\sqrt{3}y-x-2\sqrt{3}=0$ is the required equation.