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 ${30}^o$ with the positive direction of the x-axis.

Answer 1

Line $AB$ intersects the $y$-axis $2$ units above origin.

As we know that at $y$-axis, abscissa ($x$-coordinate) will be $0$ always.

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

Also line $AB$ makes an angle of $30°$ with the $x$-axis.

$\therefore$ Slope of the line $=\tan 30°=\frac{1}{\sqrt{3}}$

As we know that equation of a line passing through $(x_0,y_0)$ and having slope $m$ is-

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

Therefore equation of the line $AB$ is-

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

$\Rightarrow x-\sqrt{3}y+2=0$

Hence the required answer is $x-\sqrt{3}y+2=0$