A) \[\frac{a}{d}=\frac{b}{c}\]
B) \[c=f\]
C) \[\frac{a}{d}=\frac{b}{e}=\frac{c}{f}\]
D) \[a=d,b=e,c=f\]
Correct Answer: C
Solution :
The equations \[ax+by+c=0\]and \[dx+ey+f=0\]will represent the same straight line, if their slopes and y- intercepts are equal. \[\therefore \] \[\frac{-a}{b}=\frac{-d}{e}\]and \[\frac{-c}{b}=\frac{-f}{e}\] \[\Rightarrow \] \[\frac{a}{d}=\frac{b}{e}\] and \[\frac{b}{e}=\frac{c}{f}\] \[\Rightarrow \] \[\frac{a}{d}=\frac{b}{e}=\frac{c}{f}\]
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