The equation of the line through the point $(-1,3)$ in symmetrical form, when the angle made by the line…
The equation of the line through the point $(-1,3)$ in symmetrical form, when the angle made by the line with the positive direction of $X$-axis is $120^{\circ}$, is given by
The equation of line through the point $\left(x_1, y_1\right)$ in symmetrical form, if it's inclination with positive direction of $X$-axis is $\theta$ is
$
\frac{x-x_1}{\cos \theta}=\frac{y-y_1}{\sin \theta}=r
$
So, the equation of the line in symmetric form where $\left(x_1, y_1\right)=(-1,3)$ and $\theta=120^{\circ}$ is
$
\frac{x+1}{\cos 120^{\circ}}=\frac{y-3}{\sin 120^{\circ}}=r \Rightarrow \frac{x+1}{-1 / 2}=\frac{y-3}{\sqrt{3} / 2}=r
$