Question

The parallelism condition for two straight lines one of which is specified by the equation ax+by+c=0 the other being represented parametrically by $x=\alpha t+\beta ,y=\gamma t+\delta$ is given by

• A. $\alpha \gamma -b\alpha =0,\beta =\delta =c=0$
• B. $a\alpha -b\gamma =0,\beta =\delta =0$
• C. $a\alpha +b\gamma =0$
• D. $a\gamma =b\alpha =0$

Answer 1

The correct option is C $a\alpha +b\gamma =0$

Given lines are $ax+by+c=0$ .....(i)
and $x=\alpha t+\beta ,y=\gamma t+\delta$
After eliminating t, we get $\gamma x-\alpha y+\alpha \delta -\gamma \beta =0$ .....(ii)
For parallelism condition, $\frac{a}{\gamma }=\frac{b}{-\alpha }\Rightarrow a\alpha +b\gamma =0$ .