Question

how to recognize the figure whether it is parallel or coincident or intersecting ,by looking at the equation.

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{given}\mathrm{equations}\mathrm{are}: \\ {\mathrm{a}}_1\mathrm{x}+{\mathrm{b}}_1\mathrm{y}+{\mathrm{c}}_1=0 \\ {\mathrm{a}}_2\mathrm{x}+{\mathrm{b}}_2\mathrm{y}+{\mathrm{c}}_2=0 \\ \mathrm{Now},\mathrm{for}\mathrm{parallel}\mathrm{lines}, \\ \frac{{\mathrm{a}}_1}{{\mathrm{a}}_2}=\frac{{\mathrm{b}}_1}{{\mathrm{b}}_2}\ne \frac{{\mathrm{c}}_1}{{\mathrm{c}}_2} \\ \mathrm{For}\mathrm{intersecting}\mathrm{lines}. \\ \frac{{\mathrm{a}}_1}{{\mathrm{a}}_2}\ne \frac{{\mathrm{b}}_1}{{\mathrm{b}}_2} \\ \mathrm{For}\mathrm{coincident}\mathrm{lines} \\ \frac{{\mathrm{a}}_1}{{\mathrm{a}}_2}=\frac{{\mathrm{b}}_1}{{\mathrm{b}}_2}=\frac{{\mathrm{c}}_1}{{\mathrm{c}}_2} \end{gathered}$$