Maths > Pair of Straight Lines > 7.0 Point of intersection of lines
Pair of Straight Lines
1.0 Definition
2.0 Angle between the pair of straight lines
3.0 Bisector of angle between the lines
4.0 General equation of second degree
5.0 Angle between the lines represented by general equation
6.0 Pair of bisectors of lines represented by general equation
7.0 Point of intersection of lines
8.0 Homogenization
7.1 Easy method (without using partial differentiation)
\[\because \Delta = \left| {\begin{array}{c}a&h&g \\ h&b&f \\ g&f&c \end{array}} \right|\]
From first two rows, $$\begin{equation} \begin{aligned} a{\text{ }}h{\text{ }}g{\text{ }} \Rightarrow {\text{ }}ax + hy + g = 0 \\ h{\text{ }}b{\text{ }}f{\text{ }} \Rightarrow {\text{ }}hx + by + f = 0 \\\end{aligned} \end{equation} $$
Solve the two equations to find the point of intersection.
