Question

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

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

Answer 1

Answer: (C)

$a \alpha + b \gamma = 0$

Answer 2

Given lines are $a x + b y + c = 0$ .....(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, $\frac { a } { \gamma } = \frac { b } { - \alpha }$ ⇒ $a \alpha + b \gamma = 0$ .