Q. The parallelism condition for two straight lines one of which is specified by the equation $ax + by + c = 0$ and the other being represented parametrically by $x = \alpha t + \beta,\ y = \gamma t + \delta,$ is given by
A) $a\gamma + b\alpha = 0,\ \beta = \delta = c = 0$
B) $a\alpha - b\gamma = 0,\ \beta = \delta = 0$
C) $a\alpha + b\gamma = 0$
D) $a\gamma = b\alpha = 0$
Explanation
(c)
Give lines are $ax + by + c = 0$ …(i)
$x = \alpha t + \beta$ …(ii)
$and\ y = \gamma t + \delta$ …(iii)
On eliminating $t$, from Eqs. (ii) and (iii), we get
$\gamma x - \alpha y + \alpha\delta - \beta\gamma = 0$ …(iv)
For parallelism condition in Eqs. (i) and (iv)
$\frac{a}{\gamma} = \frac{b}{- \alpha}$
$\Rightarrow a\alpha + b\gamma = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.