A) \[(6,4)\]
B) \[(-3,3)\]
C) \[(-8,8)\]
D) \[(0,7)\]
Correct Answer: C
Solution :
Equation of AO is \[2x+3y-1+\lambda (x+2y-1)=0.\] |
Where \[\lambda =-1\]since the line passes through the origin. |
So, \[x+y=0.\]Since, AO is perpendicular to BC. So, \[(-1)\left( -\frac{a}{b} \right)=-1\]\[\Rightarrow \]\[a=-b\] |
Similarly, \[(2x+3y-1)+\mu \,\,(ax-ay-1)=0\]will be the equation of BO for \[\mu =-1.\] |
Now, BO is perpendicular to AC. |
Hence, \[\left\{ -\frac{(2-a)}{3+a} \right\}\left( -\frac{1}{2} \right)=-1\] |
Hence, \[a=-8,\]\[b=8\] |
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