The parallelism condition for two straight lines one of which is … - Vidyadip

MCQ

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
$a \alpha- b \gamma=0, \beta=\delta=0$
✓
$a \alpha+b \gamma=0$
D
$a \gamma=b \alpha=0$

✓

Answer

Correct option: C.

$a \alpha+b \gamma=0$

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

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