Pair of Straight Lines

Two or more straight lines' equations can be packaged into a single equation of degree higher than one. Given $L_1\equiv a_1x+b_1y+c_1=0$ and $L_2\equiv a_2x+b_2y+c_2=0$, a point $P(x_1,y_1)$ satisfies the product equation $(L_1)(L_2)=0$ exactly when $P$ lies on $L_1=0$ or $L_2=0$ — and no point off both lines satisfies it, since a product is zero only when at least one factor is zero. So $L_1\cdot L_2=0$ is the equation of the pair of straight lines $L_1=0$ and $L_2=0$ combined, and studying pairs of lines is naturally a matter of studying certain quadratic (second-degree) equations in $x,y$. …