Straight Line Question 281

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 [AMU 2000]

Options:

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 $

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Answer:

Correct Answer: C

Solution:

  • 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 } $ Þ $ a\alpha +b\gamma =0 $ .