# Converting Linear Equation in Standard Form to Symmetric Form

The general equation or standard equation of a straight line is:

Where $a$ and $b$ are constants and either $a \ne 0$ or $b \ne 0$.

Putting $y = 0$ in the above standard equation of a line, we have

This shows that the line is passing through the point $\left( { - \frac{c}{a},0} \right)$.

Since we have $\tan \alpha = m = - \frac{a}{b}$, by squaring ${\tan ^2}\alpha = {\left( {\frac{a}{b}} \right)^2} \Rightarrow {\tan ^2}\alpha = \frac{{{a^2}}}{{{b^2}}}$

Since the equation of a straight line in symmetric form is

Now we put ${x_1} = - \frac{c}{a},\,\,{y_1} = 0,\,\,\cos \alpha = \pm \frac{b}{{\sqrt {{a^2} + {b^2}} }},\,\,\sin \alpha = \pm \frac{a}{{\sqrt {{a^2} + {b^2}} }}$ in the standard equation of symmetric form, and we have

This is the equation of a line in symmetric form transformed from its general form or standard form of a straight line.