A) \[10x+14y+4=0\]
B) \[-10x-14y+4=0\]
C) \[-10x+14y+4=0\]
D) \[10x-14y=-4\]
Correct Answer: D
Solution :
| [d] Given equation of line is \[-5x+7y-2=0\] |
| Here, \[{{a}_{1}}=-5,\,\,{{b}_{1}}=7,\,\,{{c}_{1}}=-2\] |
| Since, condition for dependent linear equation is |
| \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}=\frac{1}{k},\] where, k is any arbitrary constant |
| \[\therefore \,\,\,\,\,\,\,\,\,\,\,-\frac{5}{{{a}_{2}}}=\frac{7}{{{b}_{2}}}=-\frac{2}{{{c}_{2}}}=\frac{1}{k}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,{{a}_{2}}=-5k,\,\,{{b}_{2}}=7k,\,\,{{c}_{2}}=-2k\] |
| Substituting \[k=2,\] we get \[{{a}_{2}}=-10,\,\,{{b}_{2}}=14\]and \[{{c}_{2}}=-4\] |
| \[\therefore \] The required equation of line becomes |
| \[-10x+14y-4=0\] |
| \[\Rightarrow \,\,\,\,10x-14y+4=0\] or \[10x-14y=-4\] |
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