A) \[(a,\,\,-b)\]
B) \[(-\,a,\,\,b)\]
C) \[(a,\,\,b)\]
D) \[(-\,a,\,\,-b)\]
Correct Answer: C
Solution :
\[x+2y=9,\] \[3x-5y=5,\] \[ax+by=1\] |
are concurrent |
\[\left| \begin{matrix} 1 & 2 & -\,9 \\ 3 & -\,5 & -\,5 \\ a & b & -1 \\ \end{matrix} \right|=0\] |
\[\Rightarrow \] \[1\,(5+5b)+2\,(-\,5a+3)-9\,(3b+5a)=0\] |
\[\Rightarrow \] \[-\,55a-22b+11=0\]\[\Rightarrow \] \[5a+2b=1\] |
Hence line \[5x+2y=1\] passes through the point (a, b) |
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