Question

1) Given that linear equation x-2y-6=0, write another linear equation in these two variables, such that the geometrical representation of the pair is so formed is :

(i) Coincident lines

(ii) Intersecting lines

Answer 1

Given, x-2y -6=0

For lines to be coincident
$\frac{{\mathrm{a}}_1}{{\mathrm{a}}_2}=\frac{{\mathrm{b}}_1}{{\mathrm{b}}_2}=\frac{{\mathrm{c}}_1}{{\mathrm{c}}_2}$
Thus, one possible option will be:2x-4y-12=0

For intersecting line
$\frac{{\mathrm{a}}_1}{{\mathrm{a}}_2}\ne \frac{\mathrm{b}1}{{\mathrm{b}}_2}$
Thus, one possible option will be:2x-y-12=0