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) \[a\gamma =b\alpha =0\]
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 \[a\alpha +b\gamma =0\].
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