A) \[10x+14y+4=0\]
B) \[-10x-14y+4=0\]
C) \[-10x+14y+4=0\]
D) \[10x-14y+4=0\]
Correct Answer: D
Solution :
| Condition for dependent linear equations |
| \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}=\frac{1}{k}\] ...(i) |
| Given equation of line is, \[-5x+7y-2=0\] |
| Here, \[{{a}_{1}}=-5,\,{{b}_{1}}=7,\,{{c}_{2}}=-2\] |
| From Eq. (i), \[-\frac{5}{{{a}_{2}}}=\frac{7}{{{b}_{2}}}=-\frac{2}{{{c}_{2}}}=\frac{1}{k}\][say] |
| \[\Rightarrow \,\,\,{{a}_{2}}=-5k,\ {{b}_{2}}=7k,\,{{c}_{2}}=-2k\] |
| where, k is any arbitrary constant |
| Putting k = 2, then \[{{a}_{2}}=-10\], \[{{b}_{2}}=14\] |
| and \[{{c}_{2}}=-4\] |
| \[\therefore \] The required equation of line becomes |
| \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\] |
| \[\Rightarrow \,\,\,\,-10x+14y-4=0\] |
| \[\Rightarrow \,\,\,\,10x-14y+4=0\] |
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