A) \[ab=ed;\,\,bf=ce\]
B) \[ae=bd;\,\,bc=ef\]
C) \[ad=bc,\,\,bf=ce\]
D) \[ae=bd,\,\,bf=ce\]
Correct Answer: D
Solution :
| [d] The given pair of equations is |
| \[ax+by+c=0\]and \[dx+ey+f=0\] |
| For coincident lines: |
| \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\,\,\,\,\,\,\,\,\,\Rightarrow \,\,\,\,\,\,\,\,\frac{a}{d}=\frac{b}{e}=\frac{c}{f}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,ae=bd\] |
| and \[bf=ce\] |
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